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Optimality Conditions for Extended Ky Fan Inequality with Cone and Affine Constraints and Their Applications

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  • Adela Capătă

    (Technical University of Cluj-Napoca)

Abstract

The purpose of this paper is to establish necessary and sufficient conditions for a point to be solution of an extended Ky Fan inequality. Using a separation theorem for convex sets, involving the quasi-interior of a convex set, we obtain optimality conditions for solutions of the generalized problem with cone and affine constraints. Then the main result is applied to vector optimization problems with cone and affine constraints and to duality theory.

Suggested Citation

  • Adela Capătă, 2012. "Optimality Conditions for Extended Ky Fan Inequality with Cone and Affine Constraints and Their Applications," Journal of Optimization Theory and Applications, Springer, vol. 152(3), pages 661-674, March.
    • Handle: RePEc:spr:joptap:v:152:y:2012:i:3:d:10.1007_s10957-011-9916-1
    DOI: 10.1007/s10957-011-9916-1
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    References listed on IDEAS

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    1. R. I. Boţ & E. R. Csetnek & A. Moldovan, 2008. "Revisiting Some Duality Theorems via the Quasirelative Interior in Convex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 139(1), pages 67-84, October.
    2. K. Kimura & J. C. Yao, 2008. "Semicontinuity of Solution Mappings of Parametric Generalized Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 138(3), pages 429-443, September.
    3. Gábor Kassay, 2010. "On Equilibrium Problems," Springer Optimization and Its Applications, in: Altannar Chinchuluun & Panos M. Pardalos & Rentsen Enkhbat & Ider Tseveendorj (ed.), Optimization and Optimal Control, pages 55-83, Springer.
    4. F. Cammaroto & B. Di Bella, 2005. "Separation Theorem Based on the Quasirelative Interior and Application to Duality Theory," Journal of Optimization Theory and Applications, Springer, vol. 125(1), pages 223-229, April.
    5. Q. Ansari & W. Oettli & D. Schläger, 1997. "A generalization of vectorial equilibria," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 46(2), pages 147-152, June.
    6. Júlia Salamon, 2010. "Closedness and Hadamard well-posedness of the solution map for parametric vector equilibrium problems," Journal of Global Optimization, Springer, vol. 47(2), pages 173-183, June.
    7. M. Bianchi & N. Hadjisavvas & S. Schaible, 1997. "Vector Equilibrium Problems with Generalized Monotone Bifunctions," Journal of Optimization Theory and Applications, Springer, vol. 92(3), pages 527-542, March.
    8. M. Bianchi & G. Kassay & R. Pini, 2009. "Well-posedness for vector equilibrium problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 70(1), pages 171-182, August.
    Full references (including those not matched with items on IDEAS)

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