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Characterizations of the Nonemptiness and Boundedness of Weakly Efficient Solution Sets of Convex Vector Optimization Problems in Real Reflexive Banach Spaces

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  • S. Deng

    (Northern Illinois University)

Abstract

Under a weak compactness assumption on the functions involved, which always holds in finite-dimensional normed linear spaces, this paper extends various characterizations of the nonemptiness and boundedness of weakly efficient solution sets of convex vector optimization problems, obtained previously by the author (Deng in J. Optim. Theory Appl. 96:123–131, 1998) in the real finite-dimensional normed linear space setting, to those in the real reflexive Banach space setting.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:140:y:2009:i:1:d:10.1007_s10957-008-9443-x
    DOI: 10.1007/s10957-008-9443-x
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    References listed on IDEAS

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    1. X. X. Huang & X. Q. Yang & K. L. Teo, 2004. "Characterizing Nonemptiness and Compactness of the Solution Set of a Convex Vector Optimization Problem with Cone Constraints and Applications," Journal of Optimization Theory and Applications, Springer, vol. 123(2), pages 391-407, November.
    2. V. Jeyakumar & G. M. Lee & N. Dinh, 2004. "Lagrange Multiplier Conditions Characterizing the Optimal Solution Sets of Cone-Constrained Convex Programs," Journal of Optimization Theory and Applications, Springer, vol. 123(1), pages 83-103, October.
    3. S. Deng, 1998. "Characterizations of the Nonemptiness and Compactness of Solution Sets in Convex Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 96(1), pages 123-131, January.
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    Cited by:

    1. 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.
    2. S. Deng, 2010. "Boundedness and Nonemptiness of the Efficient Solution Sets in Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 144(1), pages 29-42, January.
    3. César Gutiérrez & Rubén López, 2020. "On the Existence of Weak Efficient Solutions of Nonconvex Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 185(3), pages 880-902, June.
    4. Zhe Chen, 2013. "Asymptotic analysis in convex composite multiobjective optimization problems," Journal of Global Optimization, Springer, vol. 55(3), pages 507-520, March.
    5. Jiang-hua Fan & Yan Jing & Ren-you Zhong, 2015. "Nonemptiness and boundedness of solution sets for vector variational inequalities via topological method," Journal of Global Optimization, Springer, vol. 63(1), pages 181-193, September.
    6. César Gutiérrez & Rubén López & Vicente Novo, 2014. "Existence and Boundedness of Solutions in Infinite-Dimensional Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 162(2), pages 515-547, August.

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