On the convergence of the Pshenichnyi-Pironneau-Polak minimax algorithm with an active set strategy

被引：2

作者：

Polak, E. ^{[1
]}

机构：

[1] Univ Calif Berkeley, Dept Elect Engn & Comp Sci, Berkeley, CA 94720 USA

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2008年 / 138卷 / 02期

关键词：

minimax algorithms; active set strategies; convergence theorems;

D O I：

10.1007/s10957-008-9354-x

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

The purpose of this technical note is to present a proof of convergence of the Pshenichnyi-Pironneau-Polak (PPP) minimax algorithm (see Algorithm 2.4.1 in Polak, Optimization: Algorithms and Consistent Approximations, Springer, [1997]), modified to use an active set strategy. This active set strategy was formally derived in Polak (Optimization: Algorithms and Consistent Approximations, Springer, [1997]) from those used in the methods of feasible directions developed by Zoutendijk (Methods of Feasible Directions, Elsevier, [1960]) and Polak (Computational Methods in Optimization: A Unified Approach, Academic, [1971]). The resulting epsilon-Active PPP algorithm was presented as Algorithm 2.4.34, in Polak (Optimization: Algorithms and Consistent Approximations, Springer, [1997]), without any proofs.

引用

页码：305 / 309

页数：5

共 8 条

[1] On the Convergence of the Pshenichnyi-Pironneau-Polak Minimax Algorithm with an Active Set Strategy
E. Polak
[J]. Journal of Optimization Theory and Applications, 2008, 138 : 305 - 309
[2] Improved Filter-SQP Algorithm with Active Set for Constrained Minimax Problems
Luo, Zhijun
Wang, Lirong
[J]. JOURNAL OF APPLIED MATHEMATICS, 2014,
[3] An active-set algorithm and a trust-region approach in constrained minimax problem
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A. W. Aboutahoun
[J]. Computational and Applied Mathematics, 2018, 37 : 2605 - 2631
[4] An active-set algorithm and a trust-region approach in constrained minimax problem
EL-Sobky, B.
Aboutahoun, A. W.
[J]. COMPUTATIONAL & APPLIED MATHEMATICS, 2018, 37 (03): : 2605 - 2631
[5] Convergence of the primal-dual active set strategy for diagonally dominant systems
Ito, Kazufumi
Kunisch, Karl
[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2007, 46 (01) : 14 - 34
[6] An active set strategy to address the ill-conditioning of smoothing methods for solving finite linear minimax problems
Zhou, Zhengyong
Dai, Xiaoyang
[J]. JOURNAL OF GLOBAL OPTIMIZATION, 2023, 85 (02) : 421 - 439
[7] An active set strategy to address the ill-conditioning of smoothing methods for solving finite linear minimax problems
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Xiaoyang Dai
[J]. Journal of Global Optimization, 2023, 85 : 421 - 439
[8] An algorithm for quadratic l1-regularized optimization with a flexible active-set strategy
Solntsev, Stefan
Nocedal, Jorge
Byrd, Richard H.
[J]. OPTIMIZATION METHODS & SOFTWARE, 2015, 30 (06): : 1213 - 1237

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