Journal of Global Optimization

, Volume 58, Issue 4, pp 653–672 | Cite as

First order rejection tests for multiple-objective optimization

  • Alexandre Goldsztejn
  • Ferenc Domes
  • Brice Chevalier
Article

Abstract

Three rejection tests for multi-objective optimization problems based on first order optimality conditions are proposed. These tests can certify that a box does not contain any local minimizer, and thus it can be excluded from the search process. They generalize previously proposed rejection tests in several regards: Their scope include inequality and equality constrained smooth or nonsmooth multiple objective problems. Reported experiments show that they allow quite efficiently removing the cluster effect in mono-objective and multi-objective problems, which is one of the key issues in continuous global deterministic optimization.

Keywords

Multi-objective deterministic global optimization First order optimality conditions Interval analysis Branch and bound algorithm Cluster effect 

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Alexandre Goldsztejn
    • 1
  • Ferenc Domes
    • 2
  • Brice Chevalier
    • 3
  1. 1.CNRS, LINA (UMR 6241)NantesFrance
  2. 2.LINA (UMR 6241)Université de NantesNantesFrance
  3. 3.Université de NantesNantesFrance

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