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On the characterization of Pareto-optimal solutions in bicriterion optimization

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Abstract

For bicriterion optimization involving objective functionsf 1 andf 2 defined on a decision spaceX, a condition is presented under which the Pareto-optimal points can be characterized as solutions of the scalar optimization problems: Minimizef 1(x), subject tof 2(x)≤α,x ∈X, which α ranges over a certain interval. Using this condition, it is shown how the Pareto-optimal points can be so characterized in both convex and nonconvex situations.

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Authors and Affiliations

  1. Division of Mathematics, Computer Science, and Systems Design, University of Texas at San Antonio, San Antonio, Texas

    W. B. Gearhart (Associate Professor)

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  1. W. B. Gearhart
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Communicated by L. D. Berkovitz

The author gratefully acknowledges Dr. Ivan Singer, Institute of Mathematics, Rumanian Academy of Sciences, Bucharest, Rumania, for pointing out the relevance of Remark 7 in Ref. 7 to the results of this note.

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Gearhart, W.B. On the characterization of Pareto-optimal solutions in bicriterion optimization. J Optim Theory Appl 27, 301–307 (1979). https://doi.org/10.1007/BF00933233

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