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Comparative study of RPSALG algorithm for convex semi-infinite programming
Auslander, Alfred; Ferrer Biosca, Alberto; Goberna, Miguel Ángel; López Cerdá, Marco Antonio
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Universitat Politècnica de Catalunya. GNOM - Grup d´Optimització Numèrica i Modelització
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 Örst 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 di§erent variants of RPSALG which are compared with the unique publicly available SIP solver, NSIPS, on a battery of test problems.
Peer Reviewed
Àrees temàtiques de la UPC::Matemàtiques i estadística::Investigació operativa::Programació matemàtica
Convex programming
Convex semi-infinite programming
Remez-type methods
penalty methods
smoothing methods
cutting angle method.
Programació convexa
Attribution-NonCommercial-NoDerivs 3.0 Spain

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