Optimality conditions for approximate proper solutions in multiobjective optimization with polyhedral cones

  1. C. Gutiérrez 1
  2. L. Huerga 2
  3. B. Jiménez 2
  4. V. Novo 2
  1. 1 Universidad de Valladolid, España
  2. 2 Universidad Nacional de Educación a Distancia, España
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ISSN: 1863-8279,  1134-5764

Year of publication: 2020

Volume: 28

Issue: 2

Pages: 526-544

Type: Article

DOI: 10.1007/S11750-020-00546-1 DIALNET GOOGLE SCHOLAR lock_openOpen access editor

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Abstract

In this paper, we provide optimality conditions for approximate proper solutions of a multiobjective optimization problem, whose feasible set is given by a cone constraint and the ordering cone is polyhedral. A first class of optimality conditions is given by means of a nonlinear scalar Lagrangian and the second kind through a linear scalarization technique, under generalized convexity hypotheses, that lets us derive a Kuhn–Tucker multiplier rule.

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