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Constraint qualifications for convex optimization without convexity of constraints : New connections and applications to best approximation

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  • Chieu, N.H.
  • Jeyakumar, V.
  • Li, G.
  • Mohebi, H.

Abstract

We study constraint qualifications and necessary and sufficient optimality conditions for a convex optimization problem with inequality constraints where the constraint functions are continuously differentiable but they are not assumed to be convex. We present constraint qualifications under which the Karush–Kuhn–Tucker conditions are necessary and sufficient for optimality without the convexity of the constraint functions and establish new links among various known constraint qualifications that guarantee necessary Karush–Kuhn–Tucker conditions. We also present a new constraint qualification which is the weakest constraint qualification for the Karush–Kuhn–Tucker conditions to be necessary for optimality of the convex optimization problem. Consequently, we present Lagrange multiplier characterizations for the best approximation from a convex set in the face of nonconvex inequality constraints, extending corresponding known results in the literature. We finally give a table summarizing various links among the constraint qualifications.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:265:y:2018:i:1:p:19-25
    DOI: 10.1016/j.ejor.2017.07.038
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    References listed on IDEAS

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    1. 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.
    2. F. Deutsch & W. Li & J. Swetits, 1999. "Fenchel Duality and the Strong Conical Hull Intersection Property," Journal of Optimization Theory and Applications, Springer, vol. 102(3), pages 681-695, September.
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    Cited by:

    1. Kabgani, Alireza & Soleimani-damaneh, Majid, 2022. "Semi-quasidifferentiability in nonsmooth nonconvex multiobjective optimization," European Journal of Operational Research, Elsevier, vol. 299(1), pages 35-45.
    2. Thai Doan Chuong & Xinghuo Yu & Andrew Eberhard & Chaojie Li & Chen Liu, 2024. "Hierarchy relaxations for robust equilibrium constrained polynomial problems and applications to electric vehicle charging scheduling," Journal of Global Optimization, Springer, vol. 90(3), pages 781-811, November.
    3. Nguyen Canh Hung & Thai Doan Chuong & Nguyen Le Hoang Anh, 2024. "Optimality and Duality for Robust Optimization Problems Involving Intersection of Closed Sets," Journal of Optimization Theory and Applications, Springer, vol. 202(2), pages 771-794, August.

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