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Journal of Optimization Theory and Applications

, Volume 138, Issue 2, pp 305–309 | Cite as

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

  • E. Polak
TECHNICAL NOTE

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.

Keywords

Minimax algorithms Active set strategies Convergence theorems 

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References

  1. 1.
    Polak, E.: Optimization: Algorithms and Consistent Approximations. Springer, New York (1997) MATHGoogle Scholar
  2. 2.
    Zoutendijk, G.: Methods of Feasible Directions. Elsevier, Amsterdam (1960) MATHGoogle Scholar
  3. 3.
    Polak, E.: Computational Methods in Optimization: A Unified Approach. Academic, San Diego (1971) Google Scholar
  4. 4.
    Fletcher, R.: Practical Methods of Optimization. Wiley, New York (2000) Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of Electrical Engineering and Computer SciencesUniversity of California at BerkeleyBerkeleyUSA

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