Piecewise-Convex Maximization Problems: Algorithm and Computational Experiments

  • Authors:

  • Dominique Fortin;Ider Tsevendorj

  • Affiliations:

  • LIM, Centre de Mathématiques et Informatique, 39 rue Joliot-Curie - F-13453 Marseille Cedex 13, France. E-mail: fortin@lim.univ-mrs.fr;INRIA, Domaine de Voluceau, Rocquencourt, B.P. 105, 78153 Le Chesnay Cedex, France. E-mail: Ider.Tsevendorj@inria.fr

  • Venue:
  • Journal of Global Optimization
  • Year:
  • 2002

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Abstract

A function F : Rn→ R is called a piecewise convex function if it can be decomposed into F(x)=min{fj(x) ∣ j ∈M}, where fj :Rn → R is convex for all j∈ M={1,2...,m}. In this article, we provide an algorithm for solving F(x) subject to x∈D, which is based on global optimality conditions. We report first computational experiments on small examples and open up some issues to improve the checking of optimality conditions.