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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| Published in | Journal of optimization theory and applications Vol. 138; no. 2; pp. 305 - 309 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Boston
Springer US
01.08.2008
Springer Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0022-3239 1573-2878 |
| DOI | 10.1007/s10957-008-9354-x |
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| Abstract | 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. |
|---|---|
| AbstractList | 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. 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. 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 e-Active PPP algorithm was presented as Algorithm 2.4.34, in Polak (Optimization: Algorithms and Consistent Approximations, Springer, [1997]), without any proofs. 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 [straight epsilon]-Active PPP algorithm was presented as Algorithm 2.4.34, in Polak (Optimization: Algorithms and Consistent Approximations, Springer, [1997]), without any proofs. [PUBLICATION ABSTRACT] |
| Author | Polak, E. |
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| Keywords | 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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| References | PolakE.Optimization: Algorithms and Consistent Approximations1997New YorkSpringer0899.90148 ZoutendijkG.Methods of Feasible Directions1960AmsterdamElsevier0097.35408 PolakE.Computational Methods in Optimization: A Unified Approach1971San DiegoAcademic FletcherR.Practical Methods of Optimization2000New YorkWiley R. Fletcher (9354_CR4) 2000 E. Polak (9354_CR1) 1997 G. Zoutendijk (9354_CR2) 1960 E. Polak (9354_CR3) 1971 |
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| Title | On the Convergence of the Pshenichnyi-Pironneau-Polak Minimax Algorithm with an Active Set Strategy |
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