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Farkas-Type Results for Vector-Valued Functions with Applications

Author

Listed:
  • N. Dinh

    (International University, Vietnam National University - HCMC)

  • M. A. Goberna

    (University of Alicante)

  • M. A. López

    (University of Alicante
    Federation University)

  • T. H. Mo

    (Tien Giang University)

Abstract

The main purpose of this paper consists of providing characterizations of the inclusion of the solution set of a given conic system posed in a real locally convex topological space into a variety of subsets of the same space defined by means of vector-valued functions. These Farkas-type results are used to derive characterizations of the weak solutions of vector optimization problems (including multiobjective and scalar ones), vector variational inequalities, and vector equilibrium problems.

Suggested Citation

  • N. Dinh & M. A. Goberna & M. A. López & T. H. Mo, 2017. "Farkas-Type Results for Vector-Valued Functions with Applications," Journal of Optimization Theory and Applications, Springer, vol. 173(2), pages 357-390, May.
    • Handle: RePEc:spr:joptap:v:173:y:2017:i:2:d:10.1007_s10957-016-1055-2
    DOI: 10.1007/s10957-016-1055-2
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    References listed on IDEAS

    as
    1. N. Dinh & G. Vallet & M. Volle, 2014. "Functional inequalities and theorems of the alternative involving composite functions," Journal of Global Optimization, Springer, vol. 59(4), pages 837-863, August.
    2. N. Dinh & V. Jeyakumar & G. M. Lee, 2005. "Sequential Lagrangian Conditions for Convex Programs with Applications to Semidefinite Programming," Journal of Optimization Theory and Applications, Springer, vol. 125(1), pages 85-112, April.
    3. N. Dinh & V. Jeyakumar, 2014. "Rejoinder on: Farkas’ lemma: three decades of generalizations for mathematical optimization," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 41-44, April.
    4. N. Dinh & V. Jeyakumar, 2014. "Farkas’ lemma: three decades of generalizations for mathematical optimization," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 1-22, April.
    5. Radu Ioan Bot, 2010. "Conjugate Duality in Convex Optimization," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-642-04900-2, October.
    6. N. Dinh & J. Strodiot & V. Nguyen, 2010. "Duality and optimality conditions for generalized equilibrium problems involving DC functions," Journal of Global Optimization, Springer, vol. 48(2), pages 183-208, October.
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    Citations

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    Cited by:

    1. Nguyen Dinh & Dang Hai Long, 2022. "A Perturbation Approach to Vector Optimization Problems: Lagrange and Fenchel–Lagrange Duality," Journal of Optimization Theory and Applications, Springer, vol. 194(2), pages 713-748, August.
    2. Nithirat Sisarat & Rabian Wangkeeree & Gue Myung Lee, 2020. "On Set Containment Characterizations for Sets Described by Set-Valued Maps with Applications," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 824-841, March.
    3. D. H. Fang & Y. Zhang, 2018. "Extended Farkas’s Lemmas and Strong Dualities for Conic Programming Involving Composite Functions," Journal of Optimization Theory and Applications, Springer, vol. 176(2), pages 351-376, February.
    4. Nguyen Dinh & Miguel A. Goberna & Dang H. Long & Marco A. López-Cerdá, 2019. "New Farkas-Type Results for Vector-Valued Functions: A Non-abstract Approach," Journal of Optimization Theory and Applications, Springer, vol. 182(1), pages 4-29, July.

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