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## Polak, Elijah (Lucien)

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 Author ID: polak.elijah Published as: Polak, E.; Polak, Elijah; Polak, Elijah (Lucien); Polak, E. Lucein Homepage: https://www.eecs.berkeley.edu/Faculty/Homepages/polak.html External Links: MGP · dblp
 Documents Indexed: 167 Publications since 1963, including 3 Books Biographic References: 2 Publications
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#### Co-Authors

 29 single-authored 35 Mayne, David Q. 9 Royset, Johannes O. 6 Higgins, J. E. 6 Pironneau, Olivier 5 Klessig, R. W. 5 Sangiovanni-Vincentelli, Alberto L. 4 Kirjner-Neto, C. 4 Tits, André L. 4 Trahan, R. 3 Chung, Hoam 3 Cullum, Clifton D. jun. 3 Der Kiureghian, Armen 3 He, Limin 3 Qi, Liqun 3 Salcudean, Septimiu E. 3 Wiest, E. J. 2 Canon, Michael D. 2 da Cunha, N. O. 2 Gonzaga, Clovis C. 2 Harn, Ywh-Pyng 2 Lee, Seungho 2 Pister, Karl S. 2 Rumigny, N. 2 Sun, Defeng 2 Tishyadhigama, S. 2 Wuu, T. L. 1 Baker, Thomas E. 1 Balling, Richard J. 1 Becker, R. G. 1 Bhatti, M. Asghar 1 Bustany, Ismail 1 Collins, David C. 1 Essebo, Tommy 1 Evans, Robin J. 1 Foraker, Joseph 1 Glad, Torkel 1 Halkin, Hubert 1 Heunis, Andrew J. 1 Larsen, Arne Lykke 1 Lemarchand, Géraldine 1 Madhan, Akshay 1 Meisel, William S. 1 Messerli, E. J. 1 Meyer, Gerard G. L. 1 Michalska, Hannah H. 1 Nye, William T. 1 Pavel, Nicolae H. 1 Payne, Anthony N. 1 Payne, Harold J. 1 Raykov, Ivan Lyubenov 1 Ribiere, Gerard 1 Rosen, J. Ben 1 Sargent, R. W. H. 1 Sebastian, D. J. 1 Stimler, Daniel M. 1 Teodoru, I. 1 Voreadis, Alexander 1 Wardi, Y. Y. 1 Wets, Roger Jean-Baptiste 1 Wetter, Michael 1 Williamson, L. J.
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#### Serials

 33 Journal of Optimization Theory and Applications 21 IEEE Transactions on Automatic Control 13 SIAM Journal on Control and Optimization 7 SIAM Journal on Control 6 Applied Mathematics and Optimization 6 Mathematical Programming 5 Automatica 4 Computer Methods in Applied Mechanics and Engineering 4 Journal of Mathematical Analysis and Applications 4 SIAM Journal on Optimization 3 International Journal of Control 3 Mathematical Programming Study 3 SIAM Journal on Numerical Analysis 3 Computational Optimization and Applications 2 Journal of the Franklin Institute 2 IEEE Transactions on Circuits and Systems 2 Naval Research Logistics 2 Mathematical Programming. Series A. Series B 2 Revue Française d’Informatique et de Recherche Opérationnelle 1 American Mathematical Monthly 1 International Journal of Engineering Science 1 Journal of Computational and Applied Mathematics 1 Journal of Global Optimization 1 SIAM Review 1 Nonlinear Functional Analysis and Applications 1 Applied Mathematical Sciences 1 Mathematics in Science and Engineering 1 Journal of the Society for Industrial & Applied Mathematics. Series A. Control
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#### Fields

 105 Operations research, mathematical programming (90-XX) 74 Calculus of variations and optimal control; optimization (49-XX) 70 Numerical analysis (65-XX) 30 Systems theory; control (93-XX) 8 Mechanics of deformable solids (74-XX) 7 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 5 Approximations and expansions (41-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Computer science (68-XX) 2 History and biography (01-XX) 2 Real functions (26-XX) 2 Functions of a complex variable (30-XX) 2 Ordinary differential equations (34-XX) 2 Information and communication theory, circuits (94-XX) 1 Partial differential equations (35-XX) 1 Functional analysis (46-XX) 1 General topology (54-XX) 1 Statistics (62-XX) 1 Geophysics (86-XX)

#### Citations contained in zbMATH Open

134 Publications have been cited 2,292 times in 1,186 Documents Cited by Year
Note on the convergence of the conjugate gradient methods. (Note sur la convergence de méthodes de directions conjuguées.) Zbl 0174.48001
Polak, E.; Ribière, G.
1969
Optimization. Algorithms and consistent approximations. Zbl 0899.90148
Polak, Elijah
1997
On the use of models in the synthesis of optimization algorithms. Zbl 0257.90055
Polak, E.
1971
Theory of optimal control and mathematical programming. Zbl 0264.49001
Canon, Michael D.; Cullum, Clifton D. jun.; Polak, Elijah
1970
A superlinearly convergent algorithm for constrained optimization problems. Zbl 0477.90071
Mayne, D. Q.; Polak, E.
1982
Computational methods in optimization. A unified approach. (Численные методы оптимизации. Единыйи подход. Translation from the English by F. I. Ereshko. Edited by I. A. Vatel’. With a preface by N. N. Moiseev.) Zbl 0301.90040
Polak, E.
1974
Algorithms with adaptive smoothing for finite minimax problems. Zbl 1061.90117
Polak, E.; Royset, J. O.; Womersley, R. S.
2003
Constrained minimization under vector-valued criteria in finite dimensional spaces. Zbl 0154.44801
da Cunha, N. O.; Polak, E.
1967
On the extension of constrained optimization algorithms from differentiable to nondifferentiable problems. Zbl 0503.49021
Polak, E.; Mayne, D. Q.; Wardi, Y.
1983
Nondifferentiable optimization algorithm for designing control systems having singular value inequalities. Zbl 0532.49017
Polak, E.; Wardi, Y.
1982
Superlinearly convergent algorithm for min-max problems. Zbl 0724.90066
Polak, E.; Mayne, D. Q.; Higgins, J. E.
1991
Rate of convergence of a class of methods of feasible directions. Zbl 0283.65032
Pironneau, O.; Polak, E.
1973
An improved algorithm for optimization problems with functional inequality constraints. Zbl 0433.65033
Gonzaga, C.; Polak, E.; Trahan, R.
1980
On the rate of convergence of certain methods of centers. Zbl 0248.90048
Pironneau, O.; Polak, E.
1972
Combined phase I - phase II methods of feasible directions. Zbl 0407.90076
Polak, E.; Trahan, R.; Mayne, D. Q.
1979
An historical survey of computational methods in optimal control. Zbl 0274.49001
Polak, E.
1973
Constrained minimization problems in finite-dimensional spaces. Zbl 0145.34202
Canon, M.; Cullum, C.; Polak, E.
1966
Solving nonlinear inequalities in a finite number of iterations. Zbl 0419.65040
Mayne, D. Q.; Polak, E.; Heunis, A. J.
1981
Family of projected descent methods for optimization problems with simple bounds. Zbl 0886.90140
Schwartz, A.; Polak, E.
1997
An algorithm for optimization problems with functional inequality constraints. Zbl 0355.49007
Polak, Elijah; Mayne, David Q.
1976
Algorithms for finite and semi-infinite Min-Max-Min problems using adaptive smoothing techniques. Zbl 1061.90116
Polak, E.; Royset, J. O.
2003
On the global stabilization of locally convergent algorithms. Zbl 0335.49023
Polak, E.
1976
A multiplier method with automatic limitation of penalty growth. Zbl 0414.90078
1979
On constraint dropping schemes and optimality functions for a class of outer approximations algorithms. Zbl 0412.90059
Gonzaga, C.; Polak, E.
1979
Feasible directions algorithms for optimization problems with equality and inequality constraints. Zbl 0351.90067
Mayne, D. Q.; Polak, E.
1976
Consistent approximations for optimal control problems based on Runge-Kutta integration. Zbl 0861.49002
Schwartz, A.; Polak, E.
1996
Nondifferential optimization via adaptive smoothing. Zbl 0518.49024
Mayne, D. Q.; Polak, E.
1984
A quadratically convergent primal-dual algorithm with global convergence properties for solving optimization problems with equality constraints. Zbl 0351.90065
Mukai, H.; Polak, E.
1975
Outer approximation algorithm for nondifferentiable optimization problems. Zbl 0505.90068
Mayne, D. Q.; Polak, E.
1984
An outer approximations algorithm for computer-aided design problems. Zbl 0387.90094
Mayne, D. Q.; Polak, E.; Trahan, R.
1979
Efficient implementations of the Polak-Ribiere conjugate gradient algorithm. Zbl 0244.90034
Klessig, R.; Polak, E.
1972
First-order strong variation algorithms for optimal control. Zbl 0283.49014
Mayne, D. Q.; Polak, E.
1975
Theoretical and computational aspects of the optimal design centering, tolerancing, and tuning problem. Zbl 0425.90084
Polak, Elijah; Sangiovanni-Vincentelli, Alberto
1979
Relaxed controls and the convergence of optimal control algorithms. Zbl 0337.49017
Williamson, L. J.; Polak, E.
1976
An algorithm based on active sets and smoothing for discretized semi-infinite minimax problems. Zbl 1211.90283
Polak, E.; Womersley, R. S.; Yin, H. X.
2008
Klessig, R.; Polak, E.
1973
Constrained minimization under vector-valued criteria in linear topological spaces. Zbl 0223.49012
Da Cunha, N. O.; Polak, E.
1967
On the use of augmented Lagrangians in the solution of generalized semi-infinite min-max problems. Zbl 1122.90082
Polak, Elijah; Royset, Johannes O.
2005
Moving horizon control of linear systems with input saturation and plant uncertainty. I: Robustness. Zbl 0782.93050
Polak, E.; Yang, T. H.
1993
On the convergence of optimization algorithms. Zbl 0174.47906
Polak, E.
1969
Adaptive approximations and exact penalization for the solution of generalized semi-infinite min-max problems. Zbl 1042.49033
Royset, J. O.; Polak, E.; Der Kiureghian, A.
2003
Implementable algorithm for stochastic optimization using sample average approximations. Zbl 1129.90334
Royset, J. O.; Polak, E.
2004
A recursive quadratic programming algorithm for semi-infinite optimization problems. Zbl 0494.90058
Polak, E.; Tits, A. L.
1982
A generalized quadratic programming-based phase I–phase II method for inequality-constrained optimization. Zbl 0770.90049
Wiest, E. J.; Polak, E.
1992
A feasible directions algorithm for optimal control problems with control and terminal inequality constraints. Zbl 0364.49012
Polak, Elijah; Mayne, David Q.
1977
Extensions of stochastic optimization results to problems with system failure probability functions. Zbl 1154.90561
Royset, J. O.; Polak, E.
2007
On the extension of Newton’s method to semi-infinite minimax problems. Zbl 0756.90088
Polak, E.; Mayne, D. Q.; Higgins, J. E.
1992
Moving horizon control of nonlinear systems with input saturation, disturbances and plant uncertainty. Zbl 0786.93046
Yang, T. H.; Polak, E.
1993
An algorithm for bicriteria optimization based on the sensitivity function. Zbl 0308.49043
Payne, Harold J.; Polak, Elijah; Collins, David C.; Meisel, William S.
1975
On the use of consistent approximations in the solution of semi-infinite optimization and optimal control problems. Zbl 0805.90107
Polak, E.
1993
A comparative study of several general convergence conditions for algorithms modeled by point-to-set maps. Zbl 0417.90077
Tishyadhigama, S.; Polak, E.; Klessig, R.
1979
Efficient sample sizes in stochastic nonlinear programming. Zbl 1146.90042
Polak, E.; Royset, J. O.
2008
Algorithm models for nondifferentiable optimization. Zbl 0569.90073
Polak, E.; Mayne, D. Q.
1985
Basics of minimax algorithms. Zbl 0777.90061
Polak, E.
1989
A barrier function method for minimax problems. Zbl 0749.90081
Polak, E.; Higgins, J. E.; Mayne, D. Q.
1992
On the conversion of optimization problems with max-min constraints to standard optimization problems. Zbl 0917.65057
Kirjner-Neto, C.; Polak, E.
1998
An exact penalty function algorithm for optimal control problems with control and terminal equality constraints. I. Zbl 0417.49042
Mayne, D. Q.; Polak, E.
1980
A globally convergent, implementable multiplier method with automatic penalty limitation. Zbl 0445.90070
Polak, E.; Tits, A. L.
1980
Adaptive control of ARMA plants using worst-case design by semi-infinite optimization. Zbl 0618.93037
Polak, Elijah; Salcudean, S. E.; Mayne, D. Q.
1987
Minimizing pseudoconvex functions on convex compact sets. Zbl 0672.90093
Higgins, J. E.; Polak, E.
1990
Unified steerable phase I–phase II method of feasible directions for semi-infinite optimization. Zbl 0702.90087
Polak, E.; He, L.
1991
On the design of linear multivariable feedback systems via constrained nondifferentiable optimization in $$H^{\infty}$$ spaces. Zbl 0669.93058
Polak, Elijah; Salcudean, S. E.
1989
Effective diagonalization strategies for the solution of a class of optimal design problems. Zbl 0707.49016
He, Limin; Polak, Elijah
1990
On the optimal detection of an underwater intruder in a channel using unmanned underwater vehicles. Zbl 1241.90062
Chung, Hoam; Polak, Elijah; Royset, Johannes O.; Sastry, Shankar
2011
An implementable algorithm for the optimal design centering, tolerancing, and tuning problem. Zbl 0458.90062
Polak, E.
1982
Consistent approximations and approximate functions and gradients in optimal control. Zbl 1011.49020
Pironneau, Olivier; Polak, Elijah
2002
On the finite solution of nonlinear inequalities. Zbl 0404.65037
Polak, E.; Mayne, D. Q.
1979
Computer-aided design via optimization: A review. Zbl 0478.93021
Mayne, D. Q.; Polak, E.; Sangiovanni-Vincentelli, A.
1982
Design of nonlinear feedback controllers. Zbl 0481.93038
Polak, E.; Mayne, D. Q.
1981
Precision control for generalized pattern search algorithms with adaptive precision function evaluations. Zbl 1113.90148
Polak, Elijah; Wetter, Michael
2006
A dual method for optimal control problems with initial and final boundary constraints. Zbl 0238.49020
Pironneau, O.; Polak, E.
1973
A method of feasible directions using function approximations, with applications to min max problems. Zbl 0253.90046
Klessig, R.; Polak, E.
1973
A survey of methods of feasible directions for the solution of optimal control problems. Zbl 0258.49010
Polak, Elijah
1972
A globally converging secant method with applications to boundary value problems. Zbl 0286.65028
Polak, E.
1974
On second order necessary conditions of optimality. Zbl 0184.44501
Messerli, E. J.; Polak, E.
1969
Optimal control of aperiodic discrete-time systems. Zbl 0142.36302
Jordan, B. W.; Polak, E.
1965
On the use of approximations in algorithms for optimization problems with equality and inequality constraints. Zbl 0392.49017
Mukai, H.; Polak, E.
1978
A robust secant method for optimization problems with inequality constraints. Zbl 0427.49027
Polak, E.; Mayne, D. Q.
1981
A study of minimizing sequences. Zbl 0553.49017
Polak, E.; Wardi, Y. Y.
1984
Rate-preserving discretization strategies for semi-infinite programming and optimal control. Zbl 0790.49027
Polak, Elijah; He, Limin
1992
A method of centers based on barrier functions for solving optimal control problems with continuum state and control constraints. Zbl 0779.49043
Polak, E.; Yang, T. H.; Mayne, D. Q.
1993
An outer approximations approach to reliability-based optimal design of structures. Zbl 0908.90141
Kirjner-Neto, C.; Polak, E.; Der Kiureghian, A.
1998
On the convergence of sequential minimization algorithms. Zbl 0281.65044
Polak, E.; Sargent, R. W. H.; Sebastian, D. J.
1974
First-order strong variation algorithms for optimal control problems with terminal inequality constraints. Zbl 0283.49015
Polak, E.; Mayne, D. Q.
1975
Moving horizon control of linear systems with input saturation and plant uncertainty. II: Disturbance rejection and tracking. Zbl 0782.93051
Polak, E.; Yang, T. H.
1993
A second-order method for the general nonlinear programming problem. Zbl 0373.90067
Mukai, H.; Polak, E.
1978
A second-order method for unconstrained optimization. Zbl 0373.90068
Mukai, H.; Polak, E.
1978
A quadratically convergent algorithm for solving infinite dimensional inequalities. Zbl 0522.65045
Mayne, D. Q.; Polak, E.
1982
Algorithms for the design of control systems subject to singular value inequalities. Zbl 0494.49026
Mayne, D. Q.; Polak, E.
1982
A modified secant method for unconstrai ed minimization. Zbl 0287.90025
Polak, E.
1974
Abstract models for the synthesis of optimization algorithms. Zbl 0209.16704
Polak, E.; Meyer, G. G. L.
1971
An exact penalty function algorithm for control problems with state and control constraints. Zbl 0613.34051
Mayne, D. Q.; Polak, Elijah
1987
Semi-infinite optimization in engineering design. Zbl 0509.49022
Polak, E.
1983
Some sufficient conditions for continuous-linear-programming problems. Zbl 0146.41102
Larsen, A.; Polak, E.
1966
On the solution of singular value inequalities over a continuum of frequencies. Zbl 0487.49018
Polak, E.; Mayne, D. Q.
1981
An exact penalty function algorithm for optimal control problems with control and terminal equality constraints. II. Zbl 0417.49043
Mayne, D. Q.; Polak, E.
1980
Smoothing techniques for the solution of finite and semi-infinite min-max-min problems. Zbl 1066.90132
Polak, Elijah
2003
Superlinearly convergent algorithm for min-max problems. Zbl 0702.90075
Polak, E.; Mayne, D. Q.; Higgins, J. E.
1991
On the design of stabilizing compensators via semiinfinite optimization. Zbl 0669.93057
Polak, E.; Wuu, T. L.
1989
On the use of consistent approximations in boundary element-based shape optimization in the presence of uncertainty. Zbl 1173.74370
Rumigny, N.; Papadopoulos, P.; Polak, E.
2007
On the optimal detection of an underwater intruder in a channel using unmanned underwater vehicles. Zbl 1241.90062
Chung, Hoam; Polak, Elijah; Royset, Johannes O.; Sastry, Shankar
2011
On the perpetual collision-free RHC of fleets of vehicles. Zbl 1217.49025
Gonzalez, H.; Polak, E.
2010
On the use of outer approximations as an external active set strategy. Zbl 1197.90330
Chung, H.; Polak, E.; Sastry, S.
2010
An external active-set strategy for solving optimal control problems. Zbl 1367.49025
Chung, Hoam; Polak, Elijah; Sastry, Shankar
2009
An algorithm based on active sets and smoothing for discretized semi-infinite minimax problems. Zbl 1211.90283
Polak, E.; Womersley, R. S.; Yin, H. X.
2008
Efficient sample sizes in stochastic nonlinear programming. Zbl 1146.90042
Polak, E.; Royset, J. O.
2008
On the convergence of the Pshenichnyi-Pironneau-Polak minimax algorithm with an active set strategy. Zbl 1211.90282
Polak, E.
2008
Extensions of stochastic optimization results to problems with system failure probability functions. Zbl 1154.90561
Royset, J. O.; Polak, E.
2007
On the use of consistent approximations in boundary element-based shape optimization in the presence of uncertainty. Zbl 1173.74370
Rumigny, N.; Papadopoulos, P.; Polak, E.
2007
Precision control for generalized pattern search algorithms with adaptive precision function evaluations. Zbl 1113.90148
Polak, Elijah; Wetter, Michael
2006
On the use of augmented Lagrangians in the solution of generalized semi-infinite min-max problems. Zbl 1122.90082
Polak, Elijah; Royset, Johannes O.
2005
Implementable algorithm for stochastic optimization using sample average approximations. Zbl 1129.90334
Royset, J. O.; Polak, E.
2004
Algorithms with adaptive smoothing for finite minimax problems. Zbl 1061.90117
Polak, E.; Royset, J. O.; Womersley, R. S.
2003
Algorithms for finite and semi-infinite Min-Max-Min problems using adaptive smoothing techniques. Zbl 1061.90116
Polak, E.; Royset, J. O.
2003
Adaptive approximations and exact penalization for the solution of generalized semi-infinite min-max problems. Zbl 1042.49033
Royset, J. O.; Polak, E.; Der Kiureghian, A.
2003
Smoothing techniques for the solution of finite and semi-infinite min-max-min problems. Zbl 1066.90132
Polak, Elijah
2003
Dual-sampling-rate moving-horizon control of a class of linear systems with input saturation and plant uncertainty. Zbl 1040.93054
Brockwell, A.; Polak, E.; Evans, R.; Ralph, D.
2003
Consistent approximations and approximate functions and gradients in optimal control. Zbl 1011.49020
Pironneau, Olivier; Polak, Elijah
2002
Second-order algorithms for generalized finite and semi-infinite min-max problems. Zbl 1001.65064
Polak, Elijah; Qi, Liqun; Sun, Defeng
2001
On an approach to optimization problems with a probabilistic cost and or constraints. Zbl 0973.90054
Polak, Elijah; Wets, Roger J.-B.; Der Kiureghian, Armen
2000
First-order algorithms for generalized semi-infinite min-max problems. Zbl 1040.90562
Polak, Elijah; Qi, Liqun; Sun, Defeng
1999
On the conversion of optimization problems with max-min constraints to standard optimization problems. Zbl 0917.65057
Kirjner-Neto, C.; Polak, E.
1998
An outer approximations approach to reliability-based optimal design of structures. Zbl 0908.90141
Kirjner-Neto, C.; Polak, E.; Der Kiureghian, A.
1998
Globally and superlinearly convergent algorithm for minimizing a normal merit function. Zbl 0916.65051
Polak, Elijah; Qi, Liqun
1998
Optimization. Algorithms and consistent approximations. Zbl 0899.90148
Polak, Elijah
1997
Family of projected descent methods for optimization problems with simple bounds. Zbl 0886.90140
Schwartz, A.; Polak, E.
1997
Consistent approximations for optimal control problems based on Runge-Kutta integration. Zbl 0861.49002
Schwartz, A.; Polak, E.
1996
On the optimal control of systems described by evolution equations. Zbl 0822.49024
Baker, T. E.; Polak, E.
1994
An efficient algorithm for solving semi-infinite inequality problems with box constraints. Zbl 0820.90109
Mayne, D. Q.; Michalska, H.; Polak, E.
1994
Moving horizon control of linear systems with input saturation and plant uncertainty. I: Robustness. Zbl 0782.93050
Polak, E.; Yang, T. H.
1993
Moving horizon control of nonlinear systems with input saturation, disturbances and plant uncertainty. Zbl 0786.93046
Yang, T. H.; Polak, E.
1993
On the use of consistent approximations in the solution of semi-infinite optimization and optimal control problems. Zbl 0805.90107
Polak, E.
1993
A method of centers based on barrier functions for solving optimal control problems with continuum state and control constraints. Zbl 0779.49043
Polak, E.; Yang, T. H.; Mayne, D. Q.
1993
Moving horizon control of linear systems with input saturation and plant uncertainty. II: Disturbance rejection and tracking. Zbl 0782.93051
Polak, E.; Yang, T. H.
1993
A generalized quadratic programming-based phase I–phase II method for inequality-constrained optimization. Zbl 0770.90049
Wiest, E. J.; Polak, E.
1992
On the extension of Newton’s method to semi-infinite minimax problems. Zbl 0756.90088
Polak, E.; Mayne, D. Q.; Higgins, J. E.
1992
A barrier function method for minimax problems. Zbl 0749.90081
Polak, E.; Higgins, J. E.; Mayne, D. Q.
1992
Rate-preserving discretization strategies for semi-infinite programming and optimal control. Zbl 0790.49027
Polak, Elijah; He, Limin
1992
Superlinearly convergent algorithm for min-max problems. Zbl 0724.90066
Polak, E.; Mayne, D. Q.; Higgins, J. E.
1991
Unified steerable phase I–phase II method of feasible directions for semi-infinite optimization. Zbl 0702.90087
Polak, E.; He, L.
1991
Superlinearly convergent algorithm for min-max problems. Zbl 0702.90075
Polak, E.; Mayne, D. Q.; Higgins, J. E.
1991
An $$\epsilon$$-active barrier-function method for solving minimax problems. Zbl 0729.90074
Higgins, J. E.; Polak, E.
1991
Finite-termination schemes for solving semi-infinite satisfycing problems. Zbl 0793.90087
Polak, E.; He, L.
1991
On the rate of convergence of two minimax algorithms. Zbl 0793.90079
Wiest, E. J.; Polak, E.
1991
Minimizing pseudoconvex functions on convex compact sets. Zbl 0672.90093
Higgins, J. E.; Polak, E.
1990
Effective diagonalization strategies for the solution of a class of optimal design problems. Zbl 0707.49016
He, Limin; Polak, Elijah
1990
Basics of minimax algorithms. Zbl 0777.90061
Polak, E.
1989
On the design of linear multivariable feedback systems via constrained nondifferentiable optimization in $$H^{\infty}$$ spaces. Zbl 0669.93058
Polak, Elijah; Salcudean, S. E.
1989
On the design of stabilizing compensators via semiinfinite optimization. Zbl 0669.93057
Polak, E.; Wuu, T. L.
1989
Majorization: A computational complexity reduction technique in control system design. Zbl 0662.93023
Polak, Elijah; Stimler, Daniel M.
1988
Adaptive control of ARMA plants using worst-case design by semi-infinite optimization. Zbl 0618.93037
Polak, Elijah; Salcudean, S. E.; Mayne, D. Q.
1987
An exact penalty function algorithm for control problems with state and control constraints. Zbl 0613.34051
Mayne, D. Q.; Polak, Elijah
1987
Algorithms for optimization problems with exclusion constraints. Zbl 0581.90076
Mayne, D. Q.; Polak, E.
1986
Algorithm models for nondifferentiable optimization. Zbl 0569.90073
Polak, E.; Mayne, D. Q.
1985
Nondifferential optimization via adaptive smoothing. Zbl 0518.49024
Mayne, D. Q.; Polak, E.
1984
Outer approximation algorithm for nondifferentiable optimization problems. Zbl 0505.90068
Mayne, D. Q.; Polak, E.
1984
A study of minimizing sequences. Zbl 0553.49017
Polak, E.; Wardi, Y. Y.
1984
On three approaches to the construction of nondifferentiable optimization algorithms. Zbl 0545.90087
Polak, E.; Mayne, D. Q.
1984
On the extension of constrained optimization algorithms from differentiable to nondifferentiable problems. Zbl 0503.49021
Polak, E.; Mayne, D. Q.; Wardi, Y.
1983
Semi-infinite optimization in engineering design. Zbl 0509.49022
Polak, E.
1983
DELIGHT struct.: An optimization-based computer-aided design environment for structural engineering. Zbl 0494.73088
Balling, Richard J.; Pister, Karl S.; Polak, Elijah
1983
A superlinearly convergent algorithm for constrained optimization problems. Zbl 0477.90071
Mayne, D. Q.; Polak, E.
1982
Nondifferentiable optimization algorithm for designing control systems having singular value inequalities. Zbl 0532.49017
Polak, E.; Wardi, Y.
1982
A recursive quadratic programming algorithm for semi-infinite optimization problems. Zbl 0494.90058
Polak, E.; Tits, A. L.
1982
An implementable algorithm for the optimal design centering, tolerancing, and tuning problem. Zbl 0458.90062
Polak, E.
1982
Computer-aided design via optimization: A review. Zbl 0478.93021
Mayne, D. Q.; Polak, E.; Sangiovanni-Vincentelli, A.
1982
A quadratically convergent algorithm for solving infinite dimensional inequalities. Zbl 0522.65045
Mayne, D. Q.; Polak, E.
1982
Algorithms for the design of control systems subject to singular value inequalities. Zbl 0494.49026
Mayne, D. Q.; Polak, E.
1982
New convergence theorems for a class of feasible directions algorithms. Zbl 0458.90063
1982
A nondifferentiable optimization algorithm for the design of control systems subject to singular value inequalities over a frequency range. Zbl 0522.49020
Polak, E.; Wardi, Y.
1982
A cut-map algorithm for design problems with parameter tolerances. Zbl 0468.93030
Mayne, David Q.; Polak, Elijah; Voreadis, Alexander
1982
Solving nonlinear inequalities in a finite number of iterations. Zbl 0419.65040
Mayne, D. Q.; Polak, E.; Heunis, A. J.
1981
Design of nonlinear feedback controllers. Zbl 0481.93038
Polak, E.; Mayne, D. Q.
1981
A robust secant method for optimization problems with inequality constraints. Zbl 0427.49027
Polak, E.; Mayne, D. Q.
1981
On the solution of singular value inequalities over a continuum of frequencies. Zbl 0487.49018
Polak, E.; Mayne, D. Q.
1981
An improved algorithm for optimization problems with functional inequality constraints. Zbl 0433.65033
Gonzaga, C.; Polak, E.; Trahan, R.
1980
An exact penalty function algorithm for optimal control problems with control and terminal equality constraints. I. Zbl 0417.49042
Mayne, D. Q.; Polak, E.
1980
A globally convergent, implementable multiplier method with automatic penalty limitation. Zbl 0445.90070
Polak, E.; Tits, A. L.
1980
An exact penalty function algorithm for optimal control problems with control and terminal equality constraints. II. Zbl 0417.49043
Mayne, D. Q.; Polak, E.
1980
An interactive rectangle elimination method for biobjective decision making. Zbl 0435.90094
Payne, Anthony N.; Polak, Elijah
1980
Computer aided design via optimization. Zbl 0464.93026
Mayne, D. Q.; Polak, E.; Sangiovanni-Vincentelli, A.
1980
An implementable algorithm for the optimal design centering, tolerancing and tuning problem. Zbl 0438.65060
Polak, E.
1980
Optimization of control devices in base isolation systems for aseismic design. Zbl 0448.73085
Bhatti, M. A.; Pister, K. S.; Polak, E.
1980
Combined phase I - phase II methods of feasible directions. Zbl 0407.90076
Polak, E.; Trahan, R.; Mayne, D. Q.
1979
A multiplier method with automatic limitation of penalty growth. Zbl 0414.90078
1979
On constraint dropping schemes and optimality functions for a class of outer approximations algorithms. Zbl 0412.90059
Gonzaga, C.; Polak, E.
1979
An outer approximations algorithm for computer-aided design problems. Zbl 0387.90094
Mayne, D. Q.; Polak, E.; Trahan, R.
1979
Theoretical and computational aspects of the optimal design centering, tolerancing, and tuning problem. Zbl 0425.90084
Polak, Elijah; Sangiovanni-Vincentelli, Alberto
1979
A comparative study of several general convergence conditions for algorithms modeled by point-to-set maps. Zbl 0417.90077
Tishyadhigama, S.; Polak, E.; Klessig, R.
1979
On the finite solution of nonlinear inequalities. Zbl 0404.65037
Polak, E.; Mayne, D. Q.
1979
Algorithms for a class of computer-aided design problems: A review. Zbl 0412.49020
Polak, E.
1979
Theoretical aspects of the optimal design centering, tolerancing and tuning problem. Zbl 0501.49015
Polak, E.; Sangiovanni-Vincentelli, A.
1979
On the use of approximations in algorithms for optimization problems with equality and inequality constraints. Zbl 0392.49017
Mukai, H.; Polak, E.
1978
A second-order method for the general nonlinear programming problem. Zbl 0373.90067
Mukai, H.; Polak, E.
1978
A second-order method for unconstrained optimization. Zbl 0373.90068
Mukai, H.; Polak, E.
1978
Sensitivity analysis for hysteretic dynamic systems: Theory and applications. Zbl 0391.73081
Ray, D.; Pister, K. S.; Polak, E.
1978
A feasible directions algorithm for optimal control problems with control and terminal inequality constraints. Zbl 0364.49012
Polak, Elijah; Mayne, David Q.
1977
An algorithm for optimization problems with functional inequality constraints. Zbl 0355.49007
Polak, Elijah; Mayne, David Q.
1976
On the global stabilization of locally convergent algorithms. Zbl 0335.49023
Polak, E.
1976
Feasible directions algorithms for optimization problems with equality and inequality constraints. Zbl 0351.90067
Mayne, D. Q.; Polak, E.
1976
...and 34 more Documents
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#### Cited by 1,509 Authors

 37 Polak, Elijah (Lucien) 35 Jian, Jinbao 28 Teo, Kok Lay 27 Mayne, David Q. 21 Feng, Enmin 21 Royset, Johannes O. 16 Yuan, Gonglin 15 Wei, Zengxin 13 Qi, Liqun 13 Xiu, Zhilong 12 Wu, Soon-Yi 11 Hu, Qingjie 11 Lucidi, Stefano 11 Noll, Dominikus 11 Rustem, Berc 10 Andrei, Neculai 10 Dolezal, Jaroslav 10 Tang, Chunming 9 Apkarian, Pierre 9 Babaie-Kafaki, Saman 9 Shi, Zhenjun 8 Azhmyakov, Vadim 8 Sakawa, Masatoshi 8 Wang, Changyu 8 Zhu, Zhibin 7 Dai, Yu-Hong 7 Livieris, Ioannis E. 7 Pintelas, Panagiotis E. 7 Van Ackooij, Wim 7 Wang, Fusheng 7 Yang, Xiaoqi 7 Yuan, Jinlong 6 Alhawarat, Ahmad 6 DiPillo, Gianni 6 Gaffke, Norbert 6 Iiduka, Hideaki 6 Jiang, Xianzhen 6 Kostreva, Michael M. 6 Krejić, Nataša 6 Rückmann, Jan-Joachim 6 Salleh, Zabidin 6 Yin, Hongchao 6 Zhou, Weijun 5 Amini, Keyvan 5 Egerstedt, Magnus B. 5 Fang, Shu-Cherng 5 Goh, Chuen-Jin 5 Gong, Qi 5 Leong, Wah June 5 Liu, Zexian 5 Mahdavi-Amiri, Nezam 5 Pytlak, Radosław 5 Shen, Jie 5 Stein, Oliver 5 Tits, André L. 5 Tuy, Hoang 5 Wang, Lei 5 Ye, Jianxiong 5 Zheng, Haiyan 4 Bagirov, Adil M. 4 Chaney, Robin W. 4 Cheng, Wanyou 4 Dai, Zhifeng 4 Faramarzi, Parvaneh 4 Fukushima, Masao 4 Grippo, Luigi 4 Guo, Chuanhao 4 Han, Daolan 4 Henrion, René 4 Higgins, J. E. 4 Huang, Zheng-Hai 4 Kiwiel, Krzysztof Czesław 4 Krklec Jerinkić, Nataša 4 Li, Donghui 4 Li, Junxiang 4 Ling, Chen 4 Ma, Guodong 4 Mamat, Mustafa Bin 4 Nguyen van Thoai 4 Ni, Qin 4 Sahba, M. 4 Sun, Min 4 Uciński, Dariusz 4 Wardi, Yorai 4 Xiao, Yunhai 4 Xie, Jun 4 Zhang, Liansheng 4 Zhou, Jinchuan 3 Ahmed, Huda Issam 3 Aiyoshi, Eitaro 3 Auslender, Alfred 3 Bala Abubakar, Auwal 3 Bazaraa, Mokhtar S. 3 Chen, Yu 3 Chen, Zhongwen 3 Clements, David J. 3 Cullum, Jane K. 3 Diehl, Moritz Mathias 3 Dolgopolik, Maxim Vladimirovich 3 Dong, Yunda ...and 1,409 more Authors
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#### Cited in 207 Serials

 195 Journal of Optimization Theory and Applications 61 Applied Mathematics and Computation 57 Journal of Computational and Applied Mathematics 47 Automatica 37 Computational Optimization and Applications 29 Mathematical Programming. Series A. Series B 27 Optimization 26 International Journal of Control 25 Numerical Algorithms 23 Journal of Mathematical Analysis and Applications 23 European Journal of Operational Research 23 Mathematical Problems in Engineering 21 Journal of Global Optimization 20 Mathematical Programming 19 International Journal of Systems Science 18 Computer Methods in Applied Mechanics and Engineering 15 Kybernetika 13 SIAM Journal on Optimization 13 Computational and Applied Mathematics 13 Optimization Letters 12 Computers & Mathematics with Applications 12 Numerical Functional Analysis and Optimization 11 Applied Mathematics and Optimization 11 Optimization Methods & Software 11 Journal of Applied Mathematics and Computing 10 Applied Numerical Mathematics 10 Journal of Inequalities and Applications 10 Journal of Applied Mathematics 9 Journal of the Franklin Institute 9 Mathematics of Computation 9 Optimization and Engineering 8 Calcolo 8 Numerische Mathematik 8 Acta Mathematicae Applicatae Sinica. English Series 8 Applied Mathematical Modelling 8 International Journal of Robust and Nonlinear Control 8 Abstract and Applied Analysis 8 Nonlinear Analysis. Hybrid Systems 7 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 7 Journal of Industrial and Management Optimization 7 International Journal of Control, I. Series 6 Systems & Control Letters 6 Set-Valued and Variational Analysis 5 Journal of Computational Physics 5 Computing 5 Journal of Soviet Mathematics 5 Annals of Operations Research 5 International Journal of Computer Mathematics 5 Mathematical Methods of Operations Research 4 OR Spektrum 4 Computational Mechanics 4 Applied Mathematics Letters 4 Automation and Remote Control 4 4OR 4 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 4 Science China. Mathematics 3 Bulletin of the Australian Mathematical Society 3 Computers and Fluids 3 Journal of Fluid Mechanics 3 International Journal of Mathematics and Mathematical Sciences 3 International Journal for Numerical Methods in Engineering 3 Journal of Statistical Planning and Inference 3 Asia-Pacific Journal of Operational Research 3 Mathematical and Computer Modelling 3 Linear Algebra and its Applications 3 Computational Statistics and Data Analysis 3 European Journal of Control 3 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 3 Nonlinear Dynamics 3 International Journal of Applied Mathematics and Computer Science 3 Journal of Systems Science and Complexity 3 Iranian Journal of Science and Technology. Transaction A: Science 3 Journal of Mathematics 2 Journal of Engineering Mathematics 2 Fuzzy Sets and Systems 2 Mathematische Nachrichten 2 Transactions of the American Mathematical Society 2 Cybernetics and Systems 2 Operations Research Letters 2 Computers & Operations Research 2 MCSS. Mathematics of Control, Signals, and Systems 2 Journal of Scientific Computing 2 Science in China. Series A 2 Signal Processing 2 Discrete Event Dynamic Systems 2 Dynamics and Control 2 SIAM Review 2 Zeitschrift für Operations Research. Serie A: Theorie 2 Journal of Computer and Systems Sciences International 2 SIAM Journal on Scientific Computing 2 Applied Mathematics. Series B (English Edition) 2 Top 2 Complexity 2 Revista Investigación Operacional 2 INFORMS Journal on Computing 2 Journal of Vibration and Control 2 Multibody System Dynamics 2 The ANZIAM Journal 2 Structural and Multidisciplinary Optimization 2 Computational Management Science ...and 107 more Serials
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#### Cited in 43 Fields

 833 Operations research, mathematical programming (90-XX) 501 Numerical analysis (65-XX) 346 Calculus of variations and optimal control; optimization (49-XX) 198 Systems theory; control (93-XX) 40 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 36 Biology and other natural sciences (92-XX) 31 Mechanics of deformable solids (74-XX) 28 Statistics (62-XX) 25 Ordinary differential equations (34-XX) 25 Computer science (68-XX) 23 Partial differential equations (35-XX) 18 Fluid mechanics (76-XX) 16 Linear and multilinear algebra; matrix theory (15-XX) 15 Information and communication theory, circuits (94-XX) 11 Approximations and expansions (41-XX) 10 Probability theory and stochastic processes (60-XX) 9 Mechanics of particles and systems (70-XX) 8 Real functions (26-XX) 6 Operator theory (47-XX) 6 Global analysis, analysis on manifolds (58-XX) 6 Geophysics (86-XX) 5 Dynamical systems and ergodic theory (37-XX) 5 Classical thermodynamics, heat transfer (80-XX) 4 Functional analysis (46-XX) 4 Convex and discrete geometry (52-XX) 4 Differential geometry (53-XX) 3 Difference and functional equations (39-XX) 3 Manifolds and cell complexes (57-XX) 2 General and overarching topics; collections (00-XX) 2 History and biography (01-XX) 2 Functions of a complex variable (30-XX) 2 Optics, electromagnetic theory (78-XX) 2 Quantum theory (81-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 Mathematical logic and foundations (03-XX) 1 Combinatorics (05-XX) 1 Measure and integration (28-XX) 1 Special functions (33-XX) 1 Sequences, series, summability (40-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral equations (45-XX) 1 Geometry (51-XX) 1 Mathematics education (97-XX)