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Comparative study of RPSALG algorithm for convex semi-infinite programming

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  • A. Auslender
  • A. Ferrer
  • M. Goberna
  • M. López

Abstract

The Remez penalty and smoothing algorithm (RPSALG) is a unified framework for penalty and smoothing methods for solving min-max convex semi-infinite programing problems, whose convergence was analyzed in a previous paper of three of the authors. In this paper we consider a partial implementation of RPSALG for solving ordinary convex semi-infinite programming problems. Each iteration of RPSALG involves two types of auxiliary optimization problems: the first one consists of obtaining an approximate solution of some discretized convex problem, while the second one requires to solve a non-convex optimization problem involving the parametric constraints as objective function with the parameter as variable. In this paper we tackle the latter problem with a variant of the cutting angle method called ECAM, a global optimization procedure for solving Lipschitz programming problems. We implement different variants of RPSALG which are compared with the unique publicly available SIP solver, NSIPS, on a battery of test problems. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • A. Auslender & A. Ferrer & M. Goberna & M. López, 2015. "Comparative study of RPSALG algorithm for convex semi-infinite programming," Computational Optimization and Applications, Springer, vol. 60(1), pages 59-87, January.
    • Handle: RePEc:spr:coopap:v:60:y:2015:i:1:p:59-87
    DOI: 10.1007/s10589-014-9667-7
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    References listed on IDEAS

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    1. A.M. Bagirov & A.M. Rubinov, 2000. "Global Minimization of Increasing Positively Homogeneous Functions over the Unit Simplex," Annals of Operations Research, Springer, vol. 98(1), pages 171-187, December.
    2. Mark Fackrell, 2012. "A semi-infinite programming approach to identifying matrix-exponential distributions," International Journal of Systems Science, Taylor & Francis Journals, vol. 43(9), pages 1623-1631.
    3. S. Ito & Y. Liu & K.L. Teo, 2000. "A Dual Parametrization Method for Convex Semi-Infinite Programming," Annals of Operations Research, Springer, vol. 98(1), pages 189-213, December.
    4. Gleb Beliakov & Albert Ferrer, 2010. "Bounded lower subdifferentiability optimization techniques: applications," Journal of Global Optimization, Springer, vol. 47(2), pages 211-231, June.
    5. R. Tichatschke & A. Kaplan & T. Voetmann & M. Böhm, 2002. "Numerical treatment of an asset price model with non-stochastic uncertainty," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(1), pages 1-30, June.
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    Cited by:

    1. M. A. Goberna & M. A. López, 2017. "Recent contributions to linear semi-infinite optimization," 4OR, Springer, vol. 15(3), pages 221-264, September.
    2. Ariel Neufeld & Antonis Papapantoleon & Qikun Xiang, 2023. "Model-Free Bounds for Multi-Asset Options Using Option-Implied Information and Their Exact Computation," Management Science, INFORMS, vol. 69(4), pages 2051-2068, April.
    3. Groetzner, Patrick & Werner, Ralf, 2022. "Multiobjective optimization under uncertainty: A multiobjective robust (relative) regret approach," European Journal of Operational Research, Elsevier, vol. 296(1), pages 101-115.
    4. M. A. Goberna & M. A. López, 2018. "Recent contributions to linear semi-infinite optimization: an update," Annals of Operations Research, Springer, vol. 271(1), pages 237-278, December.
    5. Bo Wei & William B. Haskell & Sixiang Zhao, 2020. "The CoMirror algorithm with random constraint sampling for convex semi-infinite programming," Annals of Operations Research, Springer, vol. 295(2), pages 809-841, December.
    6. Goberna, M.A. & Jeyakumar, V. & Li, G. & Vicente-Pérez, J., 2022. "The radius of robust feasibility of uncertain mathematical programs: A Survey and recent developments," European Journal of Operational Research, Elsevier, vol. 296(3), pages 749-763.
    7. A. Ferrer & M. A. Goberna & E. González-Gutiérrez & M. I. Todorov, 2017. "A comparative note on the relaxation algorithms for the linear semi-infinite feasibility problem," Annals of Operations Research, Springer, vol. 258(2), pages 587-612, November.

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