Professor Elijah Polak
Elijah (Lucien) Polak was born August 11, 1931 in Bialystok, Poland. He is
a holocaust surviver and a veteran of the death camps at Dachau, Auschwitz,
Gros Rosen, and Buchenwald. His father perished in the camps, but his mother
survived. After the War, he worked as an apprentice blacksmith in Poland and
a clothes salesman in France. In 1949, he and his mother migrated to Australia,
where, after an eight year interruption, he resumed his education, while working
various part time jobs.
Elijah Polak received the B.S. degree in Electrical Engineering, from the
University of Melbourne, .Australia, in 1957 and the M.S. and Ph.D. degrees,
xvi OPTIMIZATION AND CONTROL WITH APPLICATIONS
both in Electrical Engineering, from the University of California, Berkeley, in
1959 and 1961, respectively.
In 1961 he married Ginette with whom he had a son and a daughter. At
present, they have 5 grandchildren, of which two are beginning to show an
interest in mathematics.
From 1957 to 1958 he was employed as an Instrument Engineer by Imperial
Chemical Industries, Australia and New Zealand, Ltd., in Melbourne, Australia.
He spent the summers of 1959 and 1960 as a Summer Student, with
I.B.M. Research Laboratories, San Jose, California, and the Fall Semester of
1964 as a Visiting Assistant Professor, at the Massachusetts Institute of Technology.
Since 1961, he has been on the faculty of the University of California,
Berkeley, where he is at present Professor Emeritus of Electrical Engineering
and Computer Sciences, as well as Professor in the Graduate School.
He was a Guggenheim Fellow in 1968 - 1969, at the Institut Blaise Pascal,
in Paris, France, and a United Kingdom Science Research Council Senior Post
Doctoral Fellow, at Imperial College, London, England, in 1972, in 1976, in
1979, in 1982, 1985, 1988, and in 1990.
His research interests lie in the development of optimization algorithms for
computer-aided design, with applications to electronic circuit design, control
system design, and structural design, as well as algorithms for optimal control
and nonsmooth optimization.
He is the author or co-author of over 250 papers as well as of four books:
Theory of Mathematical Programming and Optimal Control (with M. Canon
and C. Cullum, 1970), Notes of a First Course on Linear Systems (with E.
Wong, 1970), Computational Methods in Optimization (1971), and Optimization:
Algorithms and Consistent Approximations (1997). In addition, with L.
A. Zadeh, he co-edited System Theory (1969), and translated from the Russian
Absolute Stability of Regulator Systems, by M. A. Aizerman and F. R. Gantmacher
.
He is a Life Fellow of the Institute of Electrical and Electronic Engineers, a
member of the Society of Industrial and Applied Mathematics and a member
of the Mathematical Programming Society.
He is an Associate Editor the Journal of Optimization Theory and Applications,
and of the Journal of Computational Optimization and Applications.
Publications of Elijah Polak
A. BOOKS
1. E. Polak, "Absolute stability of regulator systems", (Translated from
Russian) (M. A. Aizerman and F. R. Gantmacher) Holden-Day, 1964.
2. L. A. Zadeh and E. Polak eds., Systems Theory, McGraw-Hill, 521 pages,
1969.
3. Canon, M. D., C. D. Cullum and E. Polak, Theory of Optimal Control
and Mathematical Programming, McGraw-Hill Co., New York, 285 pages,
1970.
4. E. Polak and E. Wong, Notes for a First Course on Linear Systems, Van
Nostrand Reinhold Co. New York, 169 pages, 1970.
5. E. Polak, Computational Methods in Optimization: A Unified Approach,
Academic Press, 329 pages, 1971.
6. E. Polak, Optimization: Algorithms and Consistent Approximations,
Springer, New Yort, 800 pages, 1997
B. PAPERS AND REPORTS
1. E. Polak, "Stability and Graphical Analysis of First-Order Pulse-Width-
Modulated Sampled-Data Regulator Systems," IRE Trans. on Automatic
Control, Vol. AC-6, No. 3, pp. 276-282, 1961.
2. E. Polak, "Minimum Time Control of Second Order Pulse-Width-Modulated
Sampled-Data Systems," ASME Trans. Journal of Basic Engineering,
Vol. 84, Series D, No. 1, pp. 101-110, 1962.
3. E. Polak and C. A. Desoer, "A Note on Lumped linear Time Invariant
Systems," IRE Trans. on Circuit Theory, pp. 282-283, 1962.
4. E. Polak, "Minimal Time Control of a Discrete System with a Nonlinear
Plant," IEEE Trans. on Automatic Control, Vol. AC-8, No. 1, pp. 49-56,
1963.
xviii OPTIMIZATION AND CONTROL WITH APPLICATIONS
5. E. Polak, "Exploratory Design of a Hydraulic Position Servo," Instrument
Society of Americal Trans., Vol. 2, Issue 3, pp. 207-215, 1963.
6. E. Polak, "On the Equivalence of Discrete Systems in Time-Optimal Control,"
ASME Trans. Journal of Basic Engineering, Series D, pp. 204-210,
1963.
7. E. Polak, C. A. Desoer, and J. Wing, "Theory of Minimum Time Discrete
Regulators," Proc. Second IFAC Congress, Paper No. 406, Basle, 1963.
8. E. Polak, "An Application of Discrete Optimal Control Theory," J. Franklin
Inst., Vol. 276, No. 2, pp. 118-127, 1963.
9. H. Kwakernaak and E. Polak, "On the Reduction of the System x =
Ax + Bu, y = c'x to its Minimal Equivalent," IEEE Trans. on Circuit
Theory, Vol. CT-10, No. 4, 1963.
10. E. Polak, "A Note on D-Decomposition Theory," IEEE Trans. on Control,
Vol. AC-9, No. 1, January 1964.
11. E. Polak, "Equivalence and Optimal Strategies for some Minimum Fuel
Discrete Systems," J. of the fianklin Inst., Vol. 277, No. 2, pp. 150-162,
February 1964.
12. E. Polak, "On the Evaluation of Optimal and Non-Optimal Control Strategies,"
IEEE Trans. on Automatic Control, Vol. AC-9, No. 2, pp. 175-
176,1964.
13. M. D. Canon and E. Polak, "Analog Circuits for Energy and Fuel Optimal
Control of Linear Discrete Systems," University of California, Berkeley,
Electronics Research Laboratory, Tech. Memo. M-95, August 1964.
14. E. Polak and B. W. Jordan, "Theory of a Class of Discrete Optimal
Control Systems," Journal of Electronics and Control, Vol. 17, No. 6,
pp. 697-711, 1964.
15. E. Polak and B. W. Jordan, "Optimal Control of Aperiodic Discrete-Time
Systems," J. SIAM Control, Vol. 2, pp. 332-346, 1965.
16. E. Polak, "Fundamentals of the Theory of Optimal Control," Mathematical
Review, Vol. 29, No. 2, pp. 404-405, 1965.
PUBLICATIONS OF ELIJAH POLAK xix
17. E. Polak, "An Algorithm for Reducing a Linear Time-Invariant Differential
System to State Form," IEEE Trans. on Automatic Control, Vol.
AC-11, NO. 3, pp. 577-580, 1966.
18. E. Polak, H. Halkin, B. W. Jordan, and J. B. Rosen, "Theory of Optimum
Discrete Time Systems," Proc. 3rd IFAC Congress, Paper No. 28B,
London, 1966.
19. E. Polak and A. Larsen, Jr., "Some Sufficient Conditions for Continuous
Linear Programming Problems," Int'l J. Eng. Science, Vol. 4, No. 5, pp.
583-603, 1966.
20. E. Polak and C. D. Cullum, "Equivalence Relations for the Classification
and Solution of Optimal Control Problems," J. SIAM Control, Vol. 4,
NO. 3, pp. 403-420, 1966.
21. E. Polak, M. D. Canon, and C. D. Cullum, "Constrained Minimization
Problems in Finite Dimensional Spaces," J. SIAM Control, Vol. 4, No.
3, pp. 528-547, 1966.
22. E. Polak and J. P. Jacob, "On the Inverse of the Operator O(.) = A(.) +
(.)B," American Mathematical Monthly, Vol. 73, No. 4, Part I, pp.
388-390, April 1966.
23. E. Polak and N. 0 . Da Cunha, "Constrained Minimization Under Vector
Valued-Criteria in Finite Dimensional Spaces," J. Mathematical Analysis
& Applications, Vol. 19, No. 1, pp. 103-124, 1967.
24. E. Polak and N. 0. Da Cunha, "Constrained Minimization Under Vector-
Valued Criteria in Linear Topological Spaces," Proc. Conference on
Mathematical Theory of Control, Los Angeles, February 1967.
25. E. Polak and K. Y. Wong, "Identification of Linear Discrete Time Systems
Using the Instrumental Variable Method," IEEE Trans. on Automatic
Control, Vol. AC-12, No. 6, pp. 707-718, 1967.
26. E. Polak, "Necessary Conditions of Optimality in Control and Programming,"
Proc. AMS Summer Seminar on the Math. of the Decision Sciences,
Stanford University, July-August 1967.
xx OPTIMIZATION AND CONTROL WITH APPLICATIONS
27. E. Polak, "An Algorithm for Computing the Jordan Canonical Form of
a Matrix," University of California, Berkeley, Electronics Research Laboratory,
Memo. M-223, September 1967.
28. E. Polak and J. P. Jacob, "On a Class of Pursuit-Evasion Problems,"
IEEE Trans. on Automatic Control, Vol. AC-12, No. 4, pp.752-755,
1967.
29. E. Polak and J. P. Jacob, "On Finite Dimensional Approximations to a
Class of Games," J. Mathematical Analysis & Applications, Vol. 21, No.
2, pp. 287-303, 1968.
30. P. L. Falb and E. Polak, "Conditions for optimality," in L. A. Zadeh and
E. Polak, eds., Systems Theory, McGraw-Hill, 1969.
31. E. Polak, "Linear Time Invariant Systems," in L. A. Zadeh and E. Polak,
eds., Systems Theory, McGraw-Hill, 1969.
32. E. Polak, "On the Removal of I11 Conditioning Effects in the Computation
of Optimal Controls," Automatica, Vol. 5, pp. 607-614, 1969.
33. E. Polak and E. J. Messerli, "On Second Order Necessary Conditions of
Optimality," SIAM J. Control, Vol. 7, No. 2, 272-291, 1969.
34. E. Polak, "On primal and Dual Methods for Solving Discrete Optimal
Control Problems," Proc. 2nd International Conference on Computing
Methods in Optimization Problems, San Remo, Italy, September 9-13,
1968. Published as: Computing Methods in Optimization Problems -2,
L. A. Zadeh, L. W. Neustadt and A. V. Balakrishnan, eds., pp. 317-331,
Academic Press, 1969.
35. E. Polak, "On the Convergence of Optimization Algorithms," Revue
Francaise dlInformatique et de Recherche Operationelle, Serie Rouge, No.
16, pp. 17-34, 1969.
36. E. Polak and G. Ribiere, "Note sur la Convergence de Methodes de Directions
Conjuguees," Revue Francaise dlInformatique et de Recherche
Operationelle, Serie Rouge, No. 16, 1969.
37. E. Polak and M. Deparis, "An Algorithm for Minimum Energy," IEEE
Trans. on Automatic Control, Vol. AC-14, No. 4, pp. 367-378, 1969.
PUBLICATIONS OF ELIJAH POLAK xxi
38. E. Polak, "On the Implementation of Conceptual Algorithms," Proc.
Nonlinear Programming Symposium, University of Wisconsin, Madison,
Wisconsin, May 4-6, 1970.
39. E. Polak and G. Meyer, "A Decomposition Algorithm for Solving a Class
of Optimal Control Problems," J. Mathematical Analysis & Applications,
Vol. 3, No. 1, pp. 118-140, 1970.
40. E. Polak, "On the use of models in the Synthesis of Optimization Algorithms,"
Differential Games and Related Topics (Proceedings of the
International Summer School on Mathematical Models of Action and Reaction,
Varenna, Italy, June 15-27, 1970), H. Kuhn and G. Szego eds.,
North Holland, Amsterdam, pp. 263-279, 1971.
41. E. Polak, H. Mukai and 0. Pironneau, "Methods of Centers and of Feasible
Directions for the Solution of Optimal Control Problems," Proc. 1971
IEEE Conference on Decision and Control, Miami Beach, Fla., Dec. 15-
17, 1971.
42. G. G. L. Meyer and E. Polak, "Abstract Models for the Synthesis of
Optimization Algorithms," SIAM J. Control, Vol. 9, No. 4, pp 547, 560,
1971.
43. 0. Pironneau and E. Polak, "On the Rate of Convergence of Certain
Methods of Centers," Mathematical Programming, Vol. 2, No. 2, pp.
230-258, 1972.
44. R. Klessig and E. Polak, "Efficient Implementations of the Polak-Ribiere
Conjugate Gradient Algorithm," SIAM J. Control, Vol. 10, No. 3, pp.
524-549, 1972.
45. E. Polak, "On a Class of Numerical Methods with an Adaptive Integration
Subprocedure for Optimal Control Problems," Proc. Fourth IFIP
Colloquium on Optimization, Santa Monica, Calif. Oct. 19-22, 1971.
Published as: Techniques of Optimization, A. V. Balakrishnan, ed., Academic
Press, pp. 89-105, 1972.
46. E. Polak, "A Survey of Methods of Feasible Directions for the Solution of
Optimal Control Problems," IEEE Transactions on Automatic Control,
Vol. AC-17, NO. 5, pp. 591-597, 1972.
xxii OPTIMIZATION AND CONTROL WITH APPLICATIONS
47. E. Polak, "A Modified Secant Method for Unconstrained Minimization,"
Proc. VIII International Symposium on Mathematical Programming,
Stanford University, Aug. 27-31, 1973.
48. 0. Pironneau and E. Polak, " A Dual Method for Optimal Control Problems
with Initial and Final Boundary Constraints," SIAM J. Control, Vol.
11, NO. 3, pp. 534-549, 1973.
49. R. Klessig and E. Polak, "An Adaptive Algorithm for Unconstrained Optimization
with Applications to Optimal Control," SIAM J. Control, Vol.
11, NO. 1, pp. 80-94, 1973.
50. 0. Pironneau and E. Polak, "Rate of Convergence of a Class of Methods
of Feasible Directions," SIAM J. Numerical Analysis, Vol. 10, No. 1,
pp. 161-174, 1973.
51. R. Klessig and E. Polak, "A Method of Feasible Directions Using Function
Approximations with Applications to Min Max Problems," J. Math.
Analysis and Applications, Vol. 41, No. 3, pp. 583-602, 1973.
52. E. Polak, "On the Use of Optimization Algorithms in the Design of Linear
Systems," University of California, Berkeley, Electronics Research Lab.
Memo. No. M377, 1973.
53. E. Polak, "A Historical Survey of Computational Methods in Optimal
Control," SIAM Review, Vol. 15, No. 2, Part 2, pp. 553-584, 1973.
54. L. J. Williamson and E. Polak, "Convergence Properties of Optimal Control
Algorithms," Proc. 1973 IEEE Conference on Decision and Control,
Dec. 5-7, 1973.
55. E. Polak, "Survey of Secant Methods for Optimization," Proc. 1973 IEEE
Conference on Decision and Control, Dec. 5-7, 1973.
56. E. Polak "A Modified Secant Method for Unconstrained Optimization,"
Mathematical Programming, Vol. 6, No. 3, pp. 264-280, 1974.
57. E. Polak "A Globally Convergent Secant Method with Applications to
Boundary Value Problems," SIAM J. Numerical Analysis, Vol. 11, No.
3, pp. 529-537, 1974.
PUBLICATIONS OF ELIJAH POLAK xxiii
58. H. J. Payne, E. Polak, D. C. Collins and S. Meisel, "An Algorithm
for Multicriteria Optimization Based on the Sensitivity Function," Proc.
1974 IEEE Conference on Decision and Control, 1974.
59. E. Polak, R. W. H.Sargent and D. J. Sebastian, "On the Convergence of
Sequential Minimization Algorithms," J. Optimization Theory and Applications,
Vol. 14, No. 4, pp. 439-442, 1974.
60. H. Mukai and E. Polak, "Approximation Techniques in Gradient Projection
Algorithms," Proc. IEEE 1974 Allerton Conference on Circuits and
Systems, Univ. of Illinois, October, 1974.
61. E. Polak and Teodoru, I., "Newton Derived Methods for Nonlinear Equations
and Inequalities," Nonlinear Programming, 0. L. Mangasarian, R.
R. Meyer and S. M. Robinson eds., Academic Press, N. Y., pp. 255-277,
1975.
62. E. Polak, "Computational Methods in Optimal Control," Proc. Conference
on Energy Related Modelling and Data Base Management, Brookhaven
National Laboratories, May 12-14, 1975.
63. R. Klessig and E. Polak, "A Survey of Convergence Theorems," Proc.
Joint National Meeting, ORSA-TIMS, Las Vegas Nevada, Nov. 17- 19,
1975.
64. H. Mukai and E. Polak, "A Quadratically Convergent Primal-Dual Algorithm
with Global Convergence Properties for solving optimization with
equality constraints," Mathematical Programming, Vol. 9, No. 3, pp.
336-350, 1975.
65. E. Polak, K. S. Pister and D. Ray, "Optimal Design of Framed Structures
Subjected to Earthquakes," Proc. Symposium on Optimization
and Engineering Design in Conjunction with the 47th national Meeting
of ORSA-TIMS, Chicago, Ill. April 30 - May 2, 1975.
66. D. Q. Mayne and E. Polak, "First Order, Strong Variations Algorithms
for Optimal Control," J. Optimization Theory and Applications, Vol. 16,
No. 314, pp. 277-301, 1975.
67. E. Polak and D. Q. Mayne, "First Order, Strong Variations Algorithms
for Optimal Control Problems with Terminal Inequality Constraints," J.
xxiv OPTIMIZATION AND CONTROL WITH APPLICATIONS
Optimization Theory and Applications, Vol. 16, No. 314, pp. 303-325,
1975.
68. E. Polak, "On the Approximation of Solutions to Multiple Criteria Decision
Making Problems," Proc. XXIIInternational Meeting TIMS, Kyoto,
Japan, July, 1975.
69. E. Polak, "On the Global Stabilization of Locally Convergent Algorithms
for Optimization and Root Finding," Proc. 6th triannaual IFAC Congress,
Boston Mass., Aug. 24-30, 1975.
70. H. J. Payne, E. Polak, D. C. Collins and S. Meisel, "An Algorithm for
Multicriteria Optimization Based on the Sensitivity Function," IEEE
Transactions on Automatic Control, Vol. AC-20, No. 4, pp. 546-548,
1975.
71. E. Polak and D. Q. Mayne, "An Algorithm for Optimization Problems
with Functional Inequality Constraints," IEEE Transactions on Automatic
Control, Vol. AC-21, No. 2, 1976.
72. E. Polak and R. Trahan, "An Algorithm for Computer Aided Design
of Control Systems," Proc. IEEE Conference on Decision and Control,
1976.
73. E. Polak and A. N. Payne, "On Multicriteria Optimization," Proc. Conference
on Directions in Decentralized Control, Many Person Games and
Large Scale Systems, Cambridge, Mass, Sept 1-3, 1975. Published as:
Directions in Large Scale Systems, Y. C. Ho and K. S. Mitter, eds.,
Plenum Press, N.Y., pp. 77-94, 1976.
74. L. J. Williamson and E. Polak, "Relaxed Controls and the Convergence
of Optimal Control Algorithms," SIAM J. Control, Vol. 14, No. 4, pp.
737-757, 1976.
75. E. Polak, "On the Approximation of Solutions to Multiple Criteria Decision
Making Problems," Multiple Criteria Decision Making: Kyoto 1975,
M. Zeleny Ed., Springer Verlag, New York, pp. 271-182, 1976.
76. E. Polak, "On the Global Stabilization of Locally Convergent Algorithms
for Optimization and Root Finding," Automatica, Vol. 12, pp. 337-342,
1976.
PUBLICATIONS OF ELIJAH POLAK xxv
77. H. Mukai and E. Polak, "On the Implementation of Reduced Gradient
Methods," Proc. 7th IFIP Conference on Optimization Techniques, Nice,
France, Sept. 8-18, 1975. Published as: Optimization Techniques: Modeling
and Optimization in the Service of Man, Jean Cea, ed., Springer
Verlag, Berlin, N.Y., Vol. 2, pp. 426-437, 1976.
78. E. Polak, K. S. Pister and D. Ray, "Optimal Design of Framed Structures
Subjected to Earthquakes," Engineering Optimization, Vol. 2, pp. 65-71,
1976.
79. D. Q. Mayne and E. Polak, "Feasible Directions Algorithms for Optimization
Problems with Equality and Inequality Constraints," Mathematical
Programming, Vol. 11, pp. 67-80, 1976.
80. D. Q. Mayne and E. Polak, "A Feasible Directions Algorithm for Optimal
Control Problems with Terminal Inequality Constraints," IEEE Transactions
on Automatic Control, Vol. AC-22, No. 5, pp. 741-751, 1977.
81. I. Teodoru Gross and E. Polak, "On the Global Stabilization of Quasi-
Newton Methods," Proc. ORSA/TIMS National Meeting, San Francisco,
May 9-11, 1977.
82. D. Ray, K. S. Pister and E. Polak, "Sensitivity Analysis for Hysteretic
Dynamical Systems: Theory and Applications," Comp. Meth. in Applied
Mechanics and Engineering, Vol. 14, pp. 179-208, 1978.
83. E. Polak, "On a Class of Computer-Aided-Design Problems," Proc. 7th
IFAC World Congress, Helsinki, Finland, June 1978.
84. H. Mukai and E. Polak, "On the Use of Approximations in Algorithms
for Optimization Problems with Equality and Inequality Constraints,"
SIAM J. Numerical Analysis, Vol. 1, No. 4, pp. 674-693, 1978.
85. E. Polak and A. Sangiovanni Vincentelli, "An Algorithm for Design Centering,
Tolerancing and Tuning," Proc. European Conference on Circuit
Theory and Design, Lausanne, Switzerland, Sept. 1978.
86. A. N. Payne and E. Polak, "An Efficient Interactive Optimization Method
for Multi-objective Design Problems," Proc. 16th Allerton Conference on
xxvi OPTIMIZATION AND CONTROL WITH APPLICATIONS
Communications, Control and Computing, Univ. of Illinois, October 4-6,
1978.
87. H. Mukai and E. Polak, "A Second Order Algorithm for Unconstrained
Optimization," J. Optimization Theory and Applications, Vol. 26, No.
4, 1978.
88. H. Mukai and E. Polak, "A second Order Algorithm for the General Nonlinear
Programming problem," J. Optimization Theory and Applications,
Vol. 26, No. 4, 1978.
89. A. N. Payne and E. Polak, "An Interactive Method for Bi-Objective Decision
Making," Proc. Second Lawrence Symposium on Systems and
Decision Sciences, Berkeley, Ca. Oct. 1978.
90. E. Polak and A. Sangiovanni Vincentelli, "On Optimization Algorithms
for Engineering Design Problems with Distributed Constraints, Tolerances
and Tuning," Proc. 1978 Joint Automatic Control Conference,
October 18, 1978.
91. M. A. Bhatti, K. S. Pister and E. Polak, "Optimal Design of an Earthquake
Isolation System," Earthquake Engineering Research Center, University
of California, Berkeley, Report No. UCBIEERC-78/22, October,
1978.
92. T. Glad and E. Polak, "A Multiplier Method with Automatic Limitation
of Penalty Growth," Mathematical Programming, Vol. 17, No. 2, pp.
140-156, 1979.
93. E. Polak, D. Q. Mayne and R. Trahan, "An Outer Approximations Algorithm
for Computer Aided Design Problems," J. Optimization Theory
and Applications, Vol. 28, No. 3, pp. 331-352, 1979.
94. E. Polak and A. Sangiovanni Vincentelli, "Theoretical and Computational
Aspects of the Optimal Design Centering, Tolerancing and Tuning Problem,"
IEEE Trans. on Circuits and Systems, Vol. CAS-26, No. 9, pp.
795-813, 1979.
95. A. N. Payne and E. Polak, "An Interactive Rectangle Elimination Method
for Multi-Objective Decision Making," IEEE Trans. on Automatic Control,
Vol. AC-25, No. 3, 1979.
PUBLICATIONS OF ELIJAH POLAK xxvii
96. S. Tishyadhigama, E. Polak and R. Klessig, "A Comparative Study of
Several General Convergence Conditions for Algorithms Modeled by Point
to Set Maps," Mathematical Programming Study 10, pp. 172-190, 1979.
97. E. Polak and D. Q. Mayne, "On the Finite Solution of Nonlinear Inequalities,"
IEEE Trans. on Automatic Control, Vol. AC-24, No. 3, pp.
443-445, 1979.
98. E. Polak, R. Trahan and D. Q. Mayne, "Combined Phase I - Phase I1
Methods of Feasible Directions," Mathematical Programming, Vol. 17,
NO. 1, pp. 32-61, 1979.
99. C. Gonzaga and E. Polak, "On Constraint Dropping Schemes and Optimality
Functions for a Class of Outer Approximations Algorithms," SIAM
J. Control and Optimization, Vol. 17, No. 4, pp. 477-493, 1979.
100. R. Trahan and E. Polak, "A Derivative Free Algorithm for a Class of
Infinitely Constrained Problems,'' IEEE Trans. on Automatic Control,
Vol. AC-25, NO. 1, pp. 54-62, 1979.
101. C. Gonzaga, E. Polak and R. Trahan, "An Improved Algorithm for Optimization
Problems with Functional Inequality Constraints," IEEE Trans.
on Automatic Control, Vol. AC-25, No. 1, pp. 49-54 1979.
102. E. Polak and D. Q. Mayne, "Algorithms for Computer Aided Design
of Control Systems by the Method of Inequalities," Proc. 18th IEEE
Conference on Decision and Control, Fort Lauderdale, Florida, Dec. 12-
14, 1979.
103. E. Polak and S. Tishyadhighama, "New Convergence Theorems for a
Class of Feasible Directions Algorithms," Proc. 18th IEEE Conference
on Decision and Control, Fort Lauderdale, Florida, Dec. 12-14, 1979.
104. E. Polak and A. Sangiovanni Vincentelli "Theoretical and Computational
Aspects of the Optimal Design Centering, Tolerancing and Tuning Problem,"
Proc. Fourth International Symposium on Mathematical Theory
of Networks and Systems, Delft University of Technology, Delft, Holland,
July 3-6, 1979.
xxviii OPTIMIZATION AND CONTROL WITH APPLICATIONS
105. E. Polak, "On the Nature of Optimization Problems in Engineering Design,"
Proc. 10th International Symposium on Mathematical Programming,
Montreal, Canada, Aug 27-30, 1979.
106. D. Q. Mayne and E. Polak, "A Superlinearly Convergent Algorithm for
Constrained Optimization Problems," Electronics Research Laboratory,
University of California, Berkeley, Memo. No. UCB/ERL M79/ 13, Jan.
1979; (presented at the 10th International Symposium on Mathematical
Programming, Montreal, Canada, Aug 27-30, 1979. Revised 151 1/ 1980,
Publication No. 78/52, Department of Computing and Control, Imperial
College, London.)
107. E. Polak "Algorithms for a Class of Computer Aided Design Problems:
a Review," Automatica, Vol. 15, pp. 531-538, 1979.
108. M. A. Bhatti, E. Polak, K. S. Pister, "OPTDYN - A General Purpose
Program for Optimization Problems with and without Dynamic Constraints,"
University of California, Berkeley, Eathquake Engineering Research
Center, Report No. UCB/EERC-79/16, July, 1979.
109. M. A. Bhatti, E. Polak, K. S. Pister, "Optimization of Control Devices
in Base isolation Systems for Aseismic Design," Proc. International IUTAM
Symposium on Structural Control, University of Waterloo, Ontario,
Canada, North Holland Pub. Co., Amsterdam, pp. 127-138, 1980.
110. E. Polak, "An Implementable Algorithm for the Optimal Design Centering,
Tolerancing and Tuning Problem," Proc. Fourth International
Symposium on Computing Methods in Applied Sciences and Engineering,
Versailles, France, Dec. 10-14, 1979. Published as: Computing Methods
in Applied Science and Engineering, R. Glowinski, J. L. Lions, ed., North
Holland, Amsterdam, pp. 499-517, 1980.
111. D. Q. Mayne and E. Polak "An Exact Penalty Function Algorithm for Optimal
Control Problems with Control and Terminal Equality Constraints,
Part 1," J. Optimization Theory and Applications, Vol. 32 No. 2, pp.
211-246, 1980.
112. D. Q. Mayne and E. Polak "An Exact Penalty Function Algorithm for Optimal
Control Problems with Control and Terminal Equality Constraints,
PUBLICATIONS OF ELIJAH POLAK xxix
Part 2," J. Optimization Theory and Applications, Vol. 32 No. 3, pp.
345-363, 1980.
113. E. Polak and A. Tits, "A Globally Convergent Implementable Multiplier
Method with Automatic Penalty Limitation," J. Appl. Math. and Optimization,
Vol. 6, pp. 335-360, 1980.
114. M. A. Bhatti, K. S. Pister, and E. Polak, "Interactive Optimal Design
of Dynamically Loaded Structures," Proc. ASCE conf on Structural
Optimization, Florida, 27-31 Oct. 1980.
115. M. A. Bhatti, K. S. Pister and E. Polak, "An Implementable Algorithm
for Computer-Aided Design Problems with or without Dynamic Constraints,"
Proc. ASME Century 2, International Computer Technology
Conference, Aug. 12-15, 1980, San Francisco. Published as: Advances in
Computer Technology - 1980, A. Sierig, ed., ASME, New York, Vol. I.,
pp. 392-400, Aug. 1980.
116. E. Polak and D. Q. Mayne, "On the Solution of Singular Value Inequalities"
Proc. 20th IEEE Conference on Decision and Control, Albuqurque,
N.M., Dec. 10-12, 1980.
117. E. Polak and D. Q. Mayne, "Design of Nonlinear Feedback Controllers,"
Proc. 20th IEEE Conference on Decision and Control, Albuqurque,
N.M., Dec. 10-12, 1980.
118. D. Q. Mayne, E. Polak and A. Voreadis, "A Cut Map Algorithm for Design
Problems with Tolerances" Proc. 20th IEEE Conference on Decision
and Control, Albuqurque, N.M., Dec. 10-12, 1980.
119. M. A. Bhatti, K. S. Pister, and E. Polak, "Interactive Optimal Design
of Dynamically Loaded Structures," Proc. 1980 ASCE National Convention,
Florida, Dec. 1980.
120. D. Q. Mayne, E. Polak and A. Sangiovanni Vincentelli, "Computer Aided
Design via Optimization," Proc. IFAC Workshop on Control Applications
of Nonlinear Programming, Denver, Colorado, June 21, 1979. Published
as: Control Applications of Nonlinear Programming, H. E. Rauch, ed.,
Pergamon Press, Oxford and New York, pp. 85-91, 1980.
xxx OPTIMIZATION AND CONTROL WITH APPLICATIONS
121. M. A. Bhatti, K. S. Pister and E. Polak, "Optimization of Control Devices
in Base Isolation Systems for Aseismic Design," Structural Control, H. H.
E. Leipholz (ed), North Holland Pub. Co. SM Publications, pp. 127-138,
1980.
122. E. Polak, "Optimization-Based Computer-Aided Design of Engineering
Systems," FOREFRONT: Research in the College of Engineering, University
of California, Berkeley, 1979/80.
123. E. Polak and D. Q. Mayne, "A Robust Secant Method for Optimization
Problems with Inequality Constraints," J. Optimization Theory and
Applications, Vol. 33, No. 4, pp. 463-467, 1981.
124. E. Polak and D. Q. Mayne, "On the Solution of Singular Value Inequalities
over a Continuum of Frequencies" IEEE Transactions on Automatic
Control, Vol. AC-26, No. 3, pp. 690-695, 1981.
125. E. Polak and D. Q. Mayne, "Design of Nonlinear Feedback Controllers,"
IEEE Transactions on Automatic Control, Vol. AC-26, No. 3, pp. 730-
733, 1981.
126. W. T. Nye, E. Polak, A. Sangiovanni-Vincentelli and A. Tits, "DELIGHT:
an Optimization-Based Computer-Aided-Design System," Proc. IEEE
Int. Symp. on Circuits and Systems, Chicago, Ill, April 24-27, 1981.
127. E. Polak and A. Tits, " On globally Stabilized Quasi-Newton Methods
for Inequality Constrained Optimization Problems," Proc. 10th IFIP
Conference on System Modeling and Optimization, New York, August
31-September 4, 1981.
128. E. Polak, "Optimization-Based Computer-Aided-Design of Control Systems,"
Proc. Joint Automatic Control Conference, University of Virginia,
Charlottesville, Virginia, June 17-19, 1981.
129. E. Polak, "Algorithms for Optimal Design," Proc. NATO Advanced
Study Institute, Univ. of Iowa, Iowa City, Ia, May 1980. Published
as: Optimization of Distributed Parameter Structures: Vol. 1, E. J.
Haug and J. Cea eds., Sijthoff & Noordhoff, pp. 586-602, 1981.
PUBLICATIONS OF ELIJAH POLAK xxxi
130. M. A. Bhatti, T. Essebo, W. Nye, K. S. Pister, E. Polak, A. Sangiovanni
Vincentelli and A. Tits, "A Software System for Optimization-
Based Computer-Aided Design" Proc. IEEE International Symp. on
Circuits and Systems, Houston, Tx, April 28-30, 1980 and also Proc.
NATO Advanced Study Institute, Univ. of Iowa, Iowa City, Ia, May
1980. Published as: Optimization of Distributed Parameter Structures:
Vol. 1, E. J. Haug and J. Cea eds., Sijthoff & Noordhoff, pp. 602-620,
1981.
131. E. Polak and Y. Wardi, "A Nondifferentiable Optimization Algorithm
for the Design of Control Systems Subject to Singular Value Inequalities
over a Frequency Range," Proceedings IFA C/8l World Congress, Kyoto,
Japan, August 24-28, 1981.
132. E. Polak, "An Implementable Algorithm for the Design Centering, Tolerancing
and Tuning Problem," J. Optimization Theory and Applications,
Vol. 35, No. 3, 1981.
133. D. Q. Mayne, E. Polak and A. J. Heunis, "Solving Nonlinear Inequalities
in a Finite Number of Iterations," J. Optimization Theory and Applications,
Vol. 33, No. 2, pp. 207-221, 1981.
134. M. A. Bhatti, V. Ciampi, K. S. Pister and E. Polak, "OPTNSR an Interactive
Software System for Optimal Design of Statically Loaded Structures
with Nonlinear Response," University of California, Berkeley, Earthquake
Engineering Research Center, Report No. UCB/EERC-81/02, 1981.
135. R. J. Balling, K. S. Pister and E. Polak, "DELIGHT.STRUCT A Computer-
Aided Design Environment for Structural Engineering," University of
California, Berkeley, Earthquake Engineering Research Center Report
No. UCB/EERC-81/19, Dec. 1981.
136. R. J. Balling, V. Ciampi, K. S. Pister and E. Polak, "Optimal Design of
Seismic-Resistant Planar Steel Frames," University of California, Berkeley,
Earthquake Engineering Research Center Report No. UCB/EERC-
81/20, Dec. 1981.
137. E. Polak, "Interactive Software for Computer-Aided-Design of Control
Systems via Optimization," Proc. 20th IEEE Conference of Decision and
Control, San Diego, Ca., pp. 408-411, Dec. 16-18, 1981.
xxxii OPTIMIZATION AND CONTROL WITH APPLICATIONS
138. M. A. Bhatti, K.S. Pister and E. Polak, "Package for Optimization-Based,
Interactive CAD," J. of the Structural Division of the A.S.C.E., Vol. 107,
No.ST11, pp. 2271-2284, 1981.
139. E. Polak, K. J. Astrom and D. Q. Mayne, "INTEROPTDYN-SISO: a Tutorial,"
University of California, Electronics Research Laboratory, Memo
UCB/ERL No. M81/99, Dec. 15, 1981.
140. D. Q. Mayne and E. Polak, "Algorithms for the Design of Control Systems
Subject to Singular Value Inequalities," Mathematical Programming
Studies, Vol. 18, pp. 112-134, 1982.
141. E. Polak and S. Tishyadhigama, "New Convergence Theorems for a Class
of Feasible Directions Algorithms," J. Optimization Theory and Applications,
Vol. 37, No. 1, pp. 33-44, 1982.
142. M. A. Bhatti, V. Ciampi, K. S. Pister and E. Polak, "An Interactive Software
System for Optimal Design of Statically and Dynamically Loaded
Structures with Nonlinear Response," Proc. of International Symposium
on Optimum Structural Design, Tucson Arizona, October 19-22, 1981.
Published as: Optimum Structural Design, R. H. Gallagher et al, eds.,
John Wiley and Sons, Chichester, England, 1982.
143. D. Q. Mayne, E. Polak and A. Voreadis, "A Cut Map Algorithm for
Design Problems with Tolerances," IEEE Trans. on Circuits and Systems,
Vol. CAS-29 NO. 1, pp. 35-46, 1982.
144. D. Q. Mayne, E. Polak and A. Sangiovanni Vincentelli, "Computer Aided
Design via Optimization: a Review," Automatica, Vol. 18, No. 2, pp.
147-154, 1982.
145. D. Q. Mayne and E. Polak, "A Superlinearly Convergent Algorithm for
Constrained Optimization Problems," Mathematical Programming Study
16, pp. 45-61, 1982.
146. E. Polak and Y. Wardi, "A Nondifferentiable Optimization Algorithm for
the Design of Control Systems Subject to Singular Value Inequalities over
a Frequency Range," Automatica, Vol. 18, No. 3, pp. 267-283, 1982.
PUBLICATIONS OF ELIJAH POLAK xxxiii
147. D. Q. Mayne and E. Polak, "Algorithms for the Design of Control Systems
Subject to Singular Value Inequalities," Mathematical Programming
Study 18, Algorithms and Theory in Filtering and Control, D. C.
Sorensen and R. J.-B. Wets, ed., North Holland, New York, pp. 112-135,
1982.
148. E. Polak and A. Tits, " A Recursive Quadratic Programming Algorithm
for Semi-Infinite Optimization Problems," J. Appl. Math. and Optimization,
Vol. 8, pp. 325-349, 1982.
149. Balling, R. J., Ciampi, V., Pister K. S. Polak, E, Sangiovanni Vincentelli,
A., Tits, A., " DELIGHT.STRUCTURE: An Interactive Software
System for Optimization-Based Computer-Aided Design of Dynamically
Loaded Structures with Nonlinear Response," Proc. ASCE Convention,
Las Vegas, 1982.
150. Balling, R. J., Ciampi, V., Pister K. S. Polak, E., "Optimal Design of
Structures Subjected to Earthquake Loading," Proc. ASCE Convention,
Las Vegas, 1982.
151. E. Polak, P. Siege1 and T. Wuu, W. T. Nye and D. Q. Mayne, "DELIGHTMIMO
an Interactive, Optimization based Multivariable Control System
Design Package," IEEE Control Systems Magazine, Vol. 2, No. 4, pp.
9-14, 1982.
152. D. Q. Mayne and E. Polak, "A Quadratically Convergent Algorithm for
Solving Infinite Dimensional Inequalities," J. of Appl. Math. and Optimization,
Vol. 9., pp. 25-40, 1982.
153. E. Polak, D.Q. Mayne and Y. Wardi, "On the Extension of Constrained
Optimization Algorithms from Differentiable to Nondifferentiable Problems,"
SIAM J. Control and Optimization, Vol. 21, No. 2, pp. 179-204,
1983.
154. Y.Y. Wardi and E. Polak, "A Nondifferentiable Optimization Algorithm
for Structural Problems with Eigenvalue Constraints," Journal of Structural
Mechanics, Vol. 11, No. 4, 1983.
155. E. Polak and D. Q. Mayne, "On Three Approaches to the Construction of
Nondifferentiable Optimization Algorithms," Proc. 11 th IFIP Conference
xxxiv OPTIMIZATION AND CONTROL WITH APPLICATIONS
on System Modelling and Optimization, Copenhagen, Denmark, July 25-
29, 1983.
156. Polak, E. and Stimler, D. M. "Optimization-Based Design of SISO Control
Systems with Uncertain Plant: Problem Formulation," University of
California, Berkeley, Electronics Research Laboratory Memo No. UCB/ERL
M83/16, 1983.
157. Polak, E. and Stimler, D. M. "Optimization-based Design of SISO Control
Systems with Uncertain Plant," Proc. IFAC Symp. on Applications
of Nonlinear Programming to Optimization and Control, San Francisco,
June 20-21, 1983.
158. Polak, E. and Stimler, D. M. "Complexity Reduction in Optimization-
Based Design of Control Systems with Uncertain Plant," Proc. American
Automatic Control Conference, San Francisco, June 22-24, 1983.
159. E. Polak, " Semi-Infinite Optimization in Engineering Design," Lecture
Notes in Economics and Mathematical Systems, Vol. 215: Semi-Infinite
Programming and Applications, A. V. Fiacco and K. 0. Kortanek, eds.,
Springer-Verlag, Berlin, New York, Tokyo, 1983.
160. E. Polak and Y. Y. Wardi, "A Study of Minimizing Sequences," Proc.
IEEE Conference on Decision and Control, San Antonio, Tx., pp. 923-
928, Dec. 1983.
161. Polak and D. Q. Mayne, "Algorithm Models for Nondifferentiable Optimization,"
Proc. IEEE Conference on Decision and Control, San Antonio,
Tx., pp. 934-939, Dec. 1983.
162. R. J. Balling, K. S. Pister and E. Polak, "DELIGHT.STRUCT A Computer-
Aided Design Environment for Structural Engineering," Computer Methods
in Applied Mechanics and Engineering, 38, pp. 237-251, 1983.
163. E. Polak, "A Modified Nyquist Stability Criterion for Use in Computer-
Aided Design," IEEE Trans. on Automatic Control, Vol. AC-29, No. 1,
pp. 91-93, 1984.
164. E. Polak and D.M. Stimler, "On the Design of Linear Control Systems
with Plant Uncertainty via Nondifferentiable Optimization," Proc. IX.
Triennial IFAC World Congress, Budapest, July 2-6, 1984.
PUBLICATIONS OF ELIJAH POLAK xxxv
165. D. Q. Mayne and E. Polak, "Outer Approximations Algorithm for Nondifferentiable
Optimization Problems," J. Optimization Theory and Applications,
Vol. 42, No. 1, pp. 19-30, 1984.
166. E. Polak, "Notes on the Mathematical Foundations of Nondifferentiable
Optimization in Engineering Design," University of California, Electronics
Research Laboratory, Memo UCB/ERL M84/15, 2 Feb. 1984.
167. E. Polak and D. Q. Mayne, "Theoretical and Software Aspects of Optimization
Based Control System Design," Proceedings of the Sixth International
Conference Analysis and Optimization of Systems, Nice, France,
June 19-22, 1984.
168. E. Polak, "A Perspective on the Use of Semi-Infinite Optimization in
Control System Design," Proc. 1984 Automatic Control Conference, San
Diego, June 1984.
169. D. Q. Mayne and E. Polak, "Nondifferentiable Optimization via Adaptive
Smoothing," J. Optimization Theory and Applications, Vol. 43, No. 4,
pp. 601-614, 1984.
170. E. Polak and Y. Y. Wardi, "A Study of Minimizing Sequences," SIAM J.
Control and Optimization, Vol. 22, No. 4, pp. 599-609, 1984.
171. M. A. Bhatti, V. Ciampi, K. S. Pister and E. Polak, "An Interactive
Software System for Optimal Design with Nonlinear Response," New Directions
in Optimum Structural Design, E. Atrek, R. H. Gallagher, K.
M. Ragsdell and 0. C. Zienkewicz eds., pp. 633-663, John Wiley and
Sons, New York, N.Y. 1984,
172. E. Polak, D. Q. Mayne and D. M. Stimler, "Control System Design via
Semi-Infinite Optimization," Proceedings of the IEEE, pp. 1777-1795,
December 1984.
173. E. Polak, S. Salcudean and D. Q. Mayne, "A Rationale for the Sequential
Optimal Redesign of Control Systems," Proc. 1985 ISCAS, pp. 835-838,
Kyoto, Japan, June 1985.
174. E. Polak, S. Salcudean and D. Q. Mayne, "A Sequential Optimal Redesign
Procedure for Linear Feedback Systems," University of California,
xxxvi OPTIMIZATION AND CONTROL WITH APPLICATIONS
Berkeley, Electronics Research laboratory Memo No. UCB/ERL M85/15,
Feb.28, 1985.
175. D. Q. Mayne and E. Polak "Algorithms for Optimization Problems with
Exclusion Constraints," Proc. 1985 IEEE Conference on Decision and
Control, Fort Lauderdale, Florida, Dec. 1985.
176. E. Polak and D. M. Stimler, "On the Efficient Formulation of the Optimal
Worst Case Control System Design Problem," University of California,
Electronics Research Laboratory Memo No. UCB/ERL M85/71, 21 August
1985.
177. E. Polak and D. Q. Mayne, "Algorithm Models for Nondifferentiable Optimization,"
SIAM J. Control and Optimization, Vol. 23, No. 3, 1985.
178. T. L. Wuu, R. G. Becker and E. Polak, "A Diagonalization Technique
for the Computation of Sensitivity Functions of Linear Time Invariant
Systems," IEEE Trans. on Automatic Control, Vol. AC-31 No. 12, pp.
1141-1143, 1986.
179. E. Polak and D. M. Stimler, "Majorization: a Computational Complexity
Reduction Technique in Control System Design," Proceedings of the
Seventh International Conference Analysis and Optimization of Systems,
Antibes, France, June, 1986.
180. D. M. Stimler and E. Polak , "Nondifferentiable Optimization in Worst
Case Control Systems Design: a Computational Example," Proc. IEEE
Control Systems Society 3rd Symposium on CACSD, Arlington, Va.,
September 24-26, 1986.
181. D. Q. Mayne and E. Polak "Algorithms for Optimization Problems with
Exclusion Constraints," J. Optimization Theory and Applications, Vol.
51, No. 3, pp. 453-474, 1986
182. E. Polak, "A Perspective on Control System Design by Means of Semi-
Infinite Optimization Algorithms," Proc. IFIP Working Conference on
Optimization Techniques, Santiago, Chile, Aug. 1984. Springer Verlag.
1987
PUBLICATIONS OF ELIJAH POLAK xxxvii
183. E. Polak and D. Q. Mayne, " Design of Multivariable Control Systems via
Semi-Infinite Optimization," Systems and Control Encyclopaedia, M. G.
Singh, editor, Pergamon Press, N.Y. 1987.
184. D. Q. Mayne and E. Polak "An Exact Penalty Function Algorithm for
Control Problems with State and Control Constraints," IEEE Trans. on
Control, Vol. AC-32, No. 5, pp. 380-388, 1987.
185. E. Polak, S. Salcudean and D. Q. Mayne, "Adaptive Control of ARMA
Plants Using Worst Case Design by Semi-Infinite Optimization, IEEE
Trans. on Automatic Control, Vol. AC-32, No. 5, pp. 388-397, 1987.
186. E. Polak, "On the Mathematical Foundations of Nondifferentiable Optimization
in Engineering Design," SIAM Review, Vo1.29, No.1 pp. 21-91,
March 1987.
187. E. Polak, T. E. Baker, T-L. Wuu and Y-P. Harn "Optimization-Based
Design of Control Systems for Flexible Structures," Proc. 4-th Annual
NASA SCOLE Workshop, Colorado Springs, December 1987.
188. S. Daijavad, E. Polak, and R-S Tsay, "A Combined Deterministic and
Random Optimization Algorithm for the Placement of Macro-Cells," Proc.
MCNC International Workshop on Placement and Routing, Research Triangle
Park, NC, May 10-13, 1988.
189. E. Polak and S. E. Salcudean, "Algorithms for Optimal Feedback Design,"
Proc. International Symposium on the Mathematical Theory of Networks
and Systems (MTNS/87), Phoenix, Arizona, June 15-19, 1987: .br C. I.
Byrnes, C. F. Martin, and R. E. Saeks eds., Linear Circuits, Systems and
Signal Processing: Theory and Applications, Elsevier Science Pub. B.V.
(North Holland), 1988.
190. T. E. Baker and E. Polak, "Computational Experiments in the Optimal
Slewing of Flexible Structures," Proc. Second NASA/Air Force Symposium
on Recent Advances in Multidisciplinary Analysis and Optimization,
Hampton, Va., Sept. 28-30, 1988.
191. E. Polak, "Minimax Algorithms for Structural Optimization," Proc. IUTAM
Symposium on Structural Optimization, Melbourne, Australia, Feb.
9 - 13, 1988.
xxxviii OPTIMIZATION AND CONTROL WITH APPLICATIONS
192. E. Polak and E. J. Wiest, "Domain Rescaling Techniques for the Solution
of Affinely Parametrized Nondifferentiable Optimal Design Problems,"
Proc. 27th IEEE Conference on Decision and Control, Austin, Tx., Dec.
7-9 1988. Dec. 1988.
193. E. Polak and D. M. Stimler, "Majorization: a Computational Complexity
Reduction Technique in Control System Design," IEEE Trans. on
Automatic Control, Vol. 33, No.11, pp 1010-1022, 1988.
194. E. Polak and S. E. Salcudean, "On The Design of Linear Multivariable
Feedback Systems via Constrained Nondifferentiable Optimization
in Hsupin f Spaces," IEEE Trans on Automatic Control, Vol. 34, No.3,
pp 268-276, 1989.
195. E. Polak and S. Wuu, "On the Design of Stabilizing Compensators via
Semi-Infinite Optimization," EEE Trans. on Control, Vol. 34, No.2, pp
196-200, 1989.
196. E. Polak, "Nonsmooth Optimization Algorithms for the Design of Controlled
Flexible Structures," Proc. AMS-SIAM-IMS Joint Summer Research
Conf. on Dynamics and Control of Multibody Systems , July
30- August 5, 1988, Bowdoin College, Brunswick, Maine. Contemporary
Mathematics Vol. 97, pp 337-371, J. E. Marsden, P. S. Krishnaprasad,
and J. C. Simo eds., American Math Soc., Providence RI, 1989.
197. E. Polak, "Basics of Minimax Algorithms," Proc. Fourth Course of the
International School of Mathematics on Nonsmooth Optimization and
Related Topics Erice, Italy, June 19 - July 8 1988. Published as (pp 343-
367): Nonsmooth Optimization and Related Topics, F. H. Clarke, V. F.
Dem'yanov and F. Giannessi eds., Plenum Press, New York, 1989.
198. L. He and E. Polak, "Effective Discretization Strategies in Optimal Design,"
Proceedings 28th IEEE Conference on Decision and Control, Tampa,
FL., December 12-14, 1989.
199. Y-P. Harn and E. Polak, "On the Design of Finite Dimensional Controllers
for Infinite Dimensional Feedback-Systems via Semi-Infinite Optimization,"
Proc. 27th IEEE Conference on Dec. and Contr., Austin,
Tx., Dec. 7-9 1988. IEEE Trans. on Automatic Control, Vol. 35, No.
10, pp. 1135-1140, 1990
PUBLICATIONS OF ELIJAH POLAK xxxix
200. J. E. Higgins and E. Polak, "Minimizing Pseudo-Convex Functions on
Convex Compact Sets," J. Optimization Theory and Applications, Vo1.65,
No.1, pp 1-28, 1990.
201. E. Polak and E. J. Wiest, "A Variable Metric Technique for the Solution
of Affinely Parametrized Nondifferentiable Optimal Design Problems," J.
Optimization Theory and Applications, Vol. 66, No. 3, pp 391-414, 1990.
202. L. He and E. Polak, "An Optimal Diagonalization Strategy for the Solution
of a Class of Optimal design Problems," IEEE, Zlans. on Automatic
Control, Vol. 35, No.3, pp 258-267, 1990.
203. T. E. Baker and E. Polak, "An Algorithm for Optimal Slewing of Flexible
Structures," University of California, Electronics Research Laboratory,
Memo UCBIERL M89/37, 11 April 1989, Revised, 4 June 1990.
204. E. Polak, T. Yang, and D. Q. Mayne, "A Method of Centers Based on
Barrier Functions for Solving Optimal Control Problems with Continuum
State and Control Constraints," Proc. 29-th IEEE Conf. on Decision and
Control, Honolulu, Hawaii, Dec. 5-7, 1990.
205. L. He and E. Polak, "Effective Diagonalization Strategies for the Solution
of a Class of Optimal Design Problems," IEEE Trans. on Automatic
Control, Vol. 35, No.3, pp 258-267, 1990.
206. D. Q. Mayne, H. Michalska and E. Polak, "An Efficient Outer Approximations
Algorithm for Solving Infinite Sets of Inequalities," Proc. 29-th
IEEE Conf. on Dec, and Control, Honolulu, Hawaii, Dec. 5-7, 1990.
207. Y-P. Harn and E. Polak, "On the Design of Finite Dimensional Controllers
for Infinite Dimensional Feedback-Systems via Semi-Infinite Optimization,"
IEEE Trans. on Automatic Control, Vol. 35, No. 10, pp.
1135-1140, 1990.
208. E. Polak, D. Q. Mayne and J. Higgins, "A Superlinearly Convergent Algorithm
for Min-Max Problems," J. Optimization Theory and Applications
Vol. 69, No.3, pp 407-439, 1991.
209. Y-P. Harn and E. Polak, "Proportional-Plus-Multiintegral Stabilizing
Compensators for a Class of MIMO Feedback Systems with Infinitexl
OPTIMIZATION AND CONTROL WITH APPLICATIONS
Dimensional Plants," IEEE Trans. on Automatic Control, Vol. 36, No.
2, pp. 207-213, 1991.
210. E. Polak and L. He, "A Unified Phase I Phase I1 Method of Feasible
Directions for Semi-infinite Optimization," J. Optimization Theory and
Applications, Vol. 69, No.1, pp 83-107, 1991.
211. J. Higgins and E. Polak, "An
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