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Descent algorithm for a class of convex nondifferentiable functions

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Abstract

We present first an ∈-descent basic method for minimizing a convex minmax problem. We consider first- and second-order information in order to generate the search direction. Preliminarily, we introduce some properties for the second-order information, the subhessian, and its characterization for max functions. The algorithm has ∈-global convergence. Finally, we give a generalization of this algorithm for an unconstrained convex problem having second-order information. In this case, we obtain global ∈-convergence.

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Authors and Affiliations

  1. Instituto de Matemática, Coordinação de Programas de Pós-Graduação de Engenharia, Universidade Federal do Rio de Janeiro (IM-COPPE/UFRJ), Rio de Janeiro, Brazil

    S. Scheimberg (Professor) & P. R. Oliveira (Professor)

Authors
  1. S. Scheimberg
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  2. P. R. Oliveira
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Additional information

Communicated by O. L. Mangasarian

This research was supported in part by CAPES (Coordinação de Aperfeiçoamento de Pessoal de Nivel Superior) and in part by the IM-COPPE/UFRJ, Brazil. The authors wish to thank Nguyen Van Hien and Jean-Jacques Strodiot for their constructive remarks on an earlier draft of the paper. This work was completed while the first author was with the Department of Mathematics of the Facultés Universitaires de Namur. The authors are also grateful for the helpful comments of two anonymous referees.

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Scheimberg, S., Oliveira, P.R. Descent algorithm for a class of convex nondifferentiable functions. J Optim Theory Appl 72, 269–297 (1992). https://doi.org/10.1007/BF00940519

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