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Constraint qualifications in convex vector semi-infinite optimization

Author

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  • Goberna, M.A.
  • Guerra-Vazquez, F.
  • Todorov, M.I.

Abstract

Convex vector (or multi-objective) semi-infinite optimization deals with the simultaneous minimization of finitely many convex scalar functions subject to infinitely many convex constraints. This paper provides characterizations of the weakly efficient, efficient and properly efficient points in terms of cones involving the data and Karush–Kuhn–Tucker conditions. The latter characterizations rely on different local and global constraint qualifications. The results in this paper generalize those obtained by the same authors on linear vector semi-infinite optimization problems.

Suggested Citation

  • Goberna, M.A. & Guerra-Vazquez, F. & Todorov, M.I., 2016. "Constraint qualifications in convex vector semi-infinite optimization," European Journal of Operational Research, Elsevier, vol. 249(1), pages 32-40.
    • Handle: RePEc:eee:ejores:v:249:y:2016:i:1:p:32-40
    DOI: 10.1016/j.ejor.2015.08.062
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    References listed on IDEAS

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    1. Todorov, Maxim Ivanov, 1996. "Kuratowski convergence of the efficient sets in the parametric linear vector semi-infinite optimization," European Journal of Operational Research, Elsevier, vol. 94(3), pages 610-617, November.
    2. Oliver Stein, 2001. "First-Order Optimality Conditions for Degenerate Index Sets in Generalized Semi-Infinite Optimization," Mathematics of Operations Research, INFORMS, vol. 26(3), pages 565-582, August.
    3. Ehrgott, Matthias & Ide, Jonas & Schöbel, Anita, 2014. "Minmax robustness for multi-objective optimization problems," European Journal of Operational Research, Elsevier, vol. 239(1), pages 17-31.
    4. Rubén Puente & Virginia Vera de Serio, 1999. "Locally Farkas-Minkowski linear inequality systems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 7(1), pages 103-121, June.
    5. Goberna, M.A. & Guerra-Vazquez, F. & Todorov, M.I., 2013. "Constraint qualifications in linear vector semi-infinite optimization," European Journal of Operational Research, Elsevier, vol. 227(1), pages 12-21.
    6. T. Chuong & N. Huy & J. Yao, 2009. "Stability of semi-infinite vector optimization problems under functional perturbations," Computational Optimization and Applications, Springer, vol. 45(4), pages 583-595, December.
    7. Chuong, T.D. & Huy, N.Q. & Yao, J.C., 2010. "Pseudo-Lipschitz property of linear semi-infinite vector optimization problems," European Journal of Operational Research, Elsevier, vol. 200(3), pages 639-644, February.
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    Cited by:

    1. M. A. Goberna & M. A. López, 2018. "Recent contributions to linear semi-infinite optimization: an update," Annals of Operations Research, Springer, vol. 271(1), pages 237-278, December.
    2. Goberna, M.A. & Jeyakumar, V. & Li, G. & Vicente-Pérez, J., 2018. "Guaranteeing highly robust weakly efficient solutions for uncertain multi-objective convex programs," European Journal of Operational Research, Elsevier, vol. 270(1), pages 40-50.
    3. Chieu, N.H. & Jeyakumar, V. & Li, G. & Mohebi, H., 2018. "Constraint qualifications for convex optimization without convexity of constraints : New connections and applications to best approximation," European Journal of Operational Research, Elsevier, vol. 265(1), pages 19-25.
    4. Marendet, Antoine & Goldsztejn, Alexandre & Chabert, Gilles & Jermann, Christophe, 2020. "A standard branch-and-bound approach for nonlinear semi-infinite problems," European Journal of Operational Research, Elsevier, vol. 282(2), pages 438-452.

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