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Existence of Optimal Points Via Improvement Sets

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  • Maurizio Chicco

    (Università di Genova)

  • Anna Rossi

    (Università di Genova)

Abstract

According to the recent definition of efficiency via improvement sets, the aim of this paper is to characterize the set of optimal points for a set. New existence results are proved in multicriteria situations, and their novelty is illustrated via several examples. Moreover, the study of an economic model is provided as an example of application of our achievements.

Suggested Citation

  • Maurizio Chicco & Anna Rossi, 2015. "Existence of Optimal Points Via Improvement Sets," Journal of Optimization Theory and Applications, Springer, vol. 167(2), pages 487-501, November.
    • Handle: RePEc:spr:joptap:v:167:y:2015:i:2:d:10.1007_s10957-015-0744-6
    DOI: 10.1007/s10957-015-0744-6
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    References listed on IDEAS

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    1. M. Chicco & F. Mignanego & L. Pusillo & S. Tijs, 2011. "Vector Optimization Problems via Improvement Sets," Journal of Optimization Theory and Applications, Springer, vol. 150(3), pages 516-529, September.
    2. P. Oppezzi & A. M. Rossi, 2006. "Existence and Convergence of Pareto Minima," Journal of Optimization Theory and Applications, Springer, vol. 128(3), pages 653-664, March.
    3. Gutiérrez, C. & Jiménez, B. & Novo, V., 2012. "Improvement sets and vector optimization," European Journal of Operational Research, Elsevier, vol. 223(2), pages 304-311.
    4. Foivos Xanthos, 2014. "Non-existence of weakly Pareto optimal allocations," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(2), pages 137-146, October.
    5. F. Flores-Bazán & C. Vera, 2006. "Characterization of the Nonemptiness and Compactness of Solution Sets in Convex and Nonconvex Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 130(2), pages 185-207, August.
    6. Gutiérrez, C. & Jiménez, B. & Novo, V., 2010. "Optimality conditions via scalarization for a new [epsilon]-efficiency concept in vector optimization problems," European Journal of Operational Research, Elsevier, vol. 201(1), pages 11-22, February.
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