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Existence of Solutions of a Vector Optimization Problem with a Generic Lower Semicontinuous Objective Function

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  • A. J. Zaslavski

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Abstract

We study a class of vector minimization problems on a complete metric space X which is identified with the corresponding complete metric space of lower semicontinuous bounded-from-below objective functions $\mathcal{A}$ . We establish the existence of a G δ everywhere dense subset ℱ of $\mathcal{A}$ such that, for any objective function belonging to ℱ, the corresponding minimization problem possesses a solution.

Suggested Citation

  • A. J. Zaslavski, 2009. "Existence of Solutions of a Vector Optimization Problem with a Generic Lower Semicontinuous Objective Function," Journal of Optimization Theory and Applications, Springer, vol. 141(1), pages 217-230, April.
    • Handle: RePEc:spr:joptap:v:141:y:2009:i:1:d:10.1007_s10957-008-9485-0
    DOI: 10.1007/s10957-008-9485-0
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    References listed on IDEAS

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    1. A. J. Zaslavski, 2008. "Generic Existence of Solutions in Vector Optimization on Metric Spaces," Journal of Optimization Theory and Applications, Springer, vol. 136(1), pages 139-153, January.
    2. ,, 2000. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 16(2), pages 287-299, April.
    3. Mario Villalobos-Arias & Carlos Coello & Onésimo Hernández-Lerma, 2006. "Asymptotic convergence of a simulated annealing algorithm for multiobjective optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(2), pages 353-362, October.
    4. T. Q. Bao & P. Gupta & B. S. Mordukhovich, 2007. "Necessary Conditions in Multiobjective Optimization with Equilibrium Constraints," Journal of Optimization Theory and Applications, Springer, vol. 135(2), pages 179-203, November.
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