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

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  • A. Y. Golubin

    (National Research University Higher School of Economics
    Russian Academy of Sciences, Design Information Technologies Center)

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.

Suggested Citation

  • A. Y. Golubin, 2015. "A Note on Optimality Conditions for Multi-objective Problems with a Euclidean Cone of Preferences," Journal of Optimization Theory and Applications, Springer, vol. 166(3), pages 791-803, September.
    • Handle: RePEc:spr:joptap:v:166:y:2015:i:3:d:10.1007_s10957-014-0698-0
    DOI: 10.1007/s10957-014-0698-0
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    References listed on IDEAS

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    1. F. Giannessi & G. Mastroeni & X. Yang, 2012. "Survey on Vector Complementarity Problems," Journal of Global Optimization, Springer, vol. 53(1), pages 53-67, May.
    2. Rastegar, Narges & Khorram, Esmaile, 2014. "A combined scalarizing method for multiobjective programming problems," European Journal of Operational Research, Elsevier, vol. 236(1), pages 229-237.
    3. A. Y. Golubin, 2006. "Pareto‐Optimal Insurance Policies in the Models with a Premium Based on the Actuarial Value," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 73(3), pages 469-487, September.
    4. S. Ruzika & M. M. Wiecek, 2005. "Approximation Methods in Multiobjective Programming," Journal of Optimization Theory and Applications, Springer, vol. 126(3), pages 473-501, September.
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