Penalty and Smoothing Methods for Convex Semi-Infinite Programming

Authors:
Alfred Auslender;Miguel A. Goberna;Marco A. López
Affiliations:
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
Venue:
Mathematics of Operations Research
Year:
2009

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Abstract

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.