Strong Duality and Solution Existence Under Minimal Assumptions in Conic Linear Programming

Nguyen Ngoc Luan () and Nguyen Dong Yen ()
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Nguyen Ngoc Luan: Hanoi National University of Education
Nguyen Dong Yen: Vietnam Academy of Science and Technology

Journal of Optimization Theory and Applications, 2024, vol. 203, issue 2, No 1, 1083-1102

Abstract: Abstract Conic linear programs in locally convex Hausdorff topological vector spaces are addressed in this paper. Solution existence for the dual problem, as well as solution existence for the primal problem, and strong duality, are proved under minimal regularity assumptions. Namely, to get the results and a Farkas-type theorem for infinite-dimensional conic linear inequalities, we employ the generalized Slater condition either for the primal problem or for the dual problem, as well as proper separation and the concept of quasi-regularity of convex sets. Illustrative examples are presented.

Keywords: Infinite-dimensional conic linear program; Dual pair; Compatible topology in the dual space; Strong duality; Solution existence; Generalized Slater condition; Quasi-regularity of convex sets; 90C25; 90C30; 90C48; 46A03; 46A20 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-023-02318-w

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