Relaxed Lagrangian duality in convex infinite optimization: reducibility and strong duality. (2nd January 2023)

• Record Type: Journal Article
• Authors: Dinh, N.; Goberna, M. A.; López-Cerdá, M. A.; Volle, M.
• Is Part Of: Optimization. Volume 72:Number 1(2023)
• Page Start: 189
• Page End: 214
• Publication Date: 2023-01-02
• Subjects: Convex infinite programming -- Lagrangian duality -- Haar duality -- reducibility; Primary 90C25 -- Secondary 49N15 -- 46N10; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2022.2031192
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : We associate with each convex optimization problem, posed on some locally convex space, with infinitely many constraints indexed by the set T, and a given non-empty family H of finite subsets of T, a suitable Lagrangian-Haar dual problem. We obtain necessary and sufficient conditions for H -reducibility, that is, equivalence to some subproblem obtained by replacing the whole index set T by some element of H . Special attention is addressed to linear optimization, infinite and semi-infinite, and to convex problems with a countable family of constraints. Results on zero H -duality gap and on H -(stable) strong duality are provided. Examples are given along the paper to illustrate the meaning of the results.