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Penalty and Smoothing Methods for Convex Semi-Infinite Programming

Université de Lyon, CNRS, UMR 5208 Institut Camille Jordan, 69622 Villeurbanne, Cedex, France, and Department of Economics, Ecole Polytechnique, F-91128 Palaiseau, Cedex, France
Department of Statistics and Operations Research, University of Alicante, 03080 Alicante, Spain
Department of Statistics and Operations Research, University of Alicante, 03080 Alicante, Spain
auslender.alfred{at}gmail.com
mgoberna{at}ua.es
marco.antonio{at}ua.es

In this paper we consider min-max convex semi-infinite programming. To solve these problems we introduce a unified framework concerning Remez-type algorithms and integral methods coupled with penalty and smoothing methods. This framework subsumes well-known classical algorithms, but also provides some new methods with interesting properties. Convergence of the primal and dual sequences are proved under minimal assumptions.

Key Words: convex semi-infinite programming; asymptotic functions; penalty methods; smoothing methods; duality
History: Received: April 2, 2007; revision received: August 29, 2008;