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A Note on Optimality Conditions for Multi-objective Problems with a Euclidean Cone of Preferences

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Abstract

The paper suggests a new—to the best of the author’s knowledge—characterization of decisions, which are optimal in the multi-objective optimization problem with respect to a definite proper preference cone, a Euclidean cone with a prescribed angular radius. The main idea is to use the angle distances between the unit vector and points of utility space. A necessary and sufficient condition for the optimality in the form of an equation is derived. The first-order necessary optimality conditions are also obtained.

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Acknowledgments

The author wishes to thank an anonimous referee and professor Giannessi for helpful comments. This research was supported by Grant 15-01-0048 from “The National Research University ‘Higher School of Economics’ Academic Fund Program”.

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Authors and Affiliations

  1. National Research University Higher School of Economics, B. Trechsvjatitelsky per., 3, Moscow, 109028, Russia

    A. Y. Golubin

  2. Russian Academy of Sciences, Design Information Technologies Center, Marshala Biryuzova Street, 7-A, Odintsovo, Moscow Region, 143000, Russia

    A. Y. Golubin

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  1. A. Y. Golubin
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Correspondence to A. Y. Golubin.

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Golubin, A.Y. A Note on Optimality Conditions for Multi-objective Problems with a Euclidean Cone of Preferences. J Optim Theory Appl 166, 791–803 (2015). https://doi.org/10.1007/s10957-014-0698-0

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  • DOI: https://doi.org/10.1007/s10957-014-0698-0

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