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Proximity measures based on KKT points for constrained multi-objective optimization

Author

Listed:
  • Gabriele Eichfelder

    (Technische Universität Ilmenau)

  • Leo Warnow

    (Technische Universität Ilmenau)

Abstract

An important aspect of optimization algorithms, for instance evolutionary algorithms, are termination criteria that measure the proximity of the found solution to the optimal solution set. A frequently used approach is the numerical verification of necessary optimality conditions such as the Karush–Kuhn–Tucker (KKT) conditions. In this paper, we present a proximity measure which characterizes the violation of the KKT conditions. It can be computed easily and is continuous in every efficient solution. Hence, it can be used as an indicator for the proximity of a certain point to the set of efficient (Edgeworth-Pareto-minimal) solutions and is well suited for algorithmic use due to its continuity properties. This is especially useful within evolutionary algorithms for candidate selection and termination, which we also illustrate numerically for some test problems.

Suggested Citation

  • Gabriele Eichfelder & Leo Warnow, 2021. "Proximity measures based on KKT points for constrained multi-objective optimization," Journal of Global Optimization, Springer, vol. 80(1), pages 63-86, May.
    • Handle: RePEc:spr:jglopt:v:80:y:2021:i:1:d:10.1007_s10898-020-00971-3
    DOI: 10.1007/s10898-020-00971-3
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    References listed on IDEAS

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    1. Giorgio Giorgi & Bienvenido Jiménez & Vicente Novo, 2016. "Approximate Karush–Kuhn–Tucker Condition in Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 171(1), pages 70-89, October.
    2. Min Feng & Shengjie Li, 2018. "An approximate strong KKT condition for multiobjective optimization," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(3), pages 489-509, October.
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    Cited by:

    1. Zachary Feinstein & Birgit Rudloff, 2022. "Deep Learning the Efficient Frontier of Convex Vector Optimization Problems," Papers 2205.07077, arXiv.org, revised Sep 2023.
    2. P. Kesarwani & P. K. Shukla & J. Dutta & K. Deb, 2022. "Approximations for Pareto and Proper Pareto solutions and their KKT conditions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 96(1), pages 123-148, August.

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