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Scalarization of vector optimization problems

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Abstract

In this paper, we investigate the scalar representation of vector optimization problems in close connection with monotonic functions. We show that it is possible to construct linear, convex, and quasiconvex representations for linear, convex, and quasiconvex vector problems, respectively. Moreover, for finding all the optimal solutions of a vector problem, it suffices to solve certain scalar representations only. The question of the continuous dependence of the solution set upon the initial vector problems and monotonic functions is also discussed.

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Authors and Affiliations

  1. Computer and Automation Institute, Hungarian Academy of Sciences, Budapest, Hungary

    D. T. Luc (Senior Researcher)

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  1. D. T. Luc
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Communicated by P. L. Yu

The author is grateful to the two referees for many valuable comments and suggestions which led to major imporvements of the paper.

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Luc, D.T. Scalarization of vector optimization problems. J Optim Theory Appl 55, 85–102 (1987). https://doi.org/10.1007/BF00939046

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  • DOI: https://doi.org/10.1007/BF00939046

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