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Gaining traction: on the convergence of an inner approximation scheme for probability maximization

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  • Csaba I. Fábián

    (John von Neumann University)

Abstract

We analyze an inner approximation scheme for probability maximization. The approach was proposed in Fábián et al. (Acta Polytech Hung 15:105–125, 2018), as an analogue of a classic dual approach in the handling of probabilistic constraints. Even a basic implementation of the maximization scheme proved usable and endured noise in gradient computations without any special effort. Moreover, the speed of convergence was not affected by approximate computation of test points. This robustness was then explained in an idealized setting. Here we work out convergence proofs and efficiency arguments for a nondegenerate normal distribution. The main message of the present paper is that the procedure gains traction as an optimal solution is approached.

Suggested Citation

  • Csaba I. Fábián, 2021. "Gaining traction: on the convergence of an inner approximation scheme for probability maximization," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 29(2), pages 491-519, June.
    • Handle: RePEc:spr:cejnor:v:29:y:2021:i:2:d:10.1007_s10100-020-00697-3
    DOI: 10.1007/s10100-020-00697-3
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    1. Darinka Dentcheva & Bogumila Lai & Andrzej Ruszczyński, 2004. "Dual methods for probabilistic optimization problems ," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 60(2), pages 331-346, October.
    2. David G. Luenberger & Yinyu Ye, 2008. "Linear and Nonlinear Programming," International Series in Operations Research and Management Science, Springer, edition 0, number 978-0-387-74503-9, December.
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