On the Convergence of the Pshenichnyi-Pironneau-Polak Minimax Algorithm with an Active Set Strategy

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 strat...

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Bibliographic Details
Published inJournal of optimization theory and applications Vol. 138; no. 2; pp. 305 - 309
Main Author Polak, E.
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.08.2008
Springer
Springer Nature B.V
Subjects
Algorithms
Applications of Mathematics
Applied sciences
Approximation
Calculus of Variations and Optimal Control; Optimization
Computation
Convergence
Engineering
Exact sciences and technology
Mathematical programming
Mathematics
Mathematics and Statistics
Minimax technique
Nonlinear programming
Operational research and scientific management
Operational research. Management science
Operations Research/Decision Theory
Optimization
Optimization algorithms
Proving
Strategy
Studies
Technical Note
Theory of Computation
Active set strategies
Minimax algorithms
Convergence theorems
Minimax problem
Feasible direction method
Minimax method
Minimax strategy
Minimax algorithms .Active set strategies .Convergence theorems
Approximation algorithm
Ellipsoid
Optimization
Convergence
Mathematical programming
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ISSN0022-3239
1573-2878
DOI10.1007/s10957-008-9354-x

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Summary: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 ε -Active PPP algorithm was presented as Algorithm 2.4.34, in Polak (Optimization: Algorithms and Consistent Approximations, Springer, [ 1997 ]), without any proofs.
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-008-9354-x