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Improvement Sets and Convergence of Optimal Points

Author

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  • Pirro Oppezzi

    (DIMA, Università di Genova)

  • Anna Rossi

    (DIME, Università di Genova)

Abstract

The aim of this paper is to give sufficient conditions for the existence of optimal points with respect to an improvement set, in the framework of Banach spaces and by using a recent definition of such sets, given by Chicco et al. and by Gutiérrez et al. The study of an economic model is provided as example of application of our achievements. The lower and upper convergences of optimal points of a convergent sequence of sets, in finite and infinite dimensional settings, are also considered, improving previous results. Finally, some sufficient conditions for the stability of optimal points are developed, discussing their importance via several examples.

Suggested Citation

  • Pirro Oppezzi & Anna Rossi, 2015. "Improvement Sets and Convergence of Optimal Points," Journal of Optimization Theory and Applications, Springer, vol. 165(2), pages 405-419, May.
    • Handle: RePEc:spr:joptap:v:165:y:2015:i:2:d:10.1007_s10957-014-0669-5
    DOI: 10.1007/s10957-014-0669-5
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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. Monique Florenzano & Pascal Gourdel & Alejandro Jofré, 2006. "Supporting weakly Pareto optimal allocations in infinite dimensional nonconvex economies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(3), pages 549-564, November.
    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. Aliprantis, Charalambos D. & Florenzano, Monique & Tourky, Rabee, 2006. "Production equilibria," Journal of Mathematical Economics, Elsevier, vol. 42(4-5), pages 406-421, August.
    5. S. Deng, 2009. "Characterizations of the Nonemptiness and Boundedness of Weakly Efficient Solution Sets of Convex Vector Optimization Problems in Real Reflexive Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 140(1), pages 1-7, January.
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    Cited by:

    1. Nguyen Quang Huy & Do Sang Kim & Nguyen Van Tuyen, 2017. "Existence Theorems in Vector Optimization with Generalized Order," Journal of Optimization Theory and Applications, Springer, vol. 174(3), pages 728-745, September.
    2. Zhiang Zhou & Wang Chen & Xinmin Yang, 2019. "Scalarizations and Optimality of Constrained Set-Valued Optimization Using Improvement Sets and Image Space Analysis," Journal of Optimization Theory and Applications, Springer, vol. 183(3), pages 944-962, December.

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