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

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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.

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References

  1. Polak, E.: Optimization: Algorithms and Consistent Approximations. Springer, New York (1997)

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  2. Zoutendijk, G.: Methods of Feasible Directions. Elsevier, Amsterdam (1960)

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  3. Polak, E.: Computational Methods in Optimization: A Unified Approach. Academic, San Diego (1971)

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  4. Fletcher, R.: Practical Methods of Optimization. Wiley, New York (2000)

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Authors and Affiliations

  1. Department of Electrical Engineering and Computer Sciences, University of California at Berkeley, Berkeley, CA, USA

    E. Polak

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  1. E. Polak
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Correspondence to E. Polak.

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Polak, E. On the Convergence of the Pshenichnyi-Pironneau-Polak Minimax Algorithm with an Active Set Strategy. J Optim Theory Appl 138, 305–309 (2008). https://doi.org/10.1007/s10957-008-9354-x

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  • DOI: https://doi.org/10.1007/s10957-008-9354-x

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