A new approach to strong duality for composite vector optimization problems. (3rd August 2021)

• Record Type: Journal Article
• Authors: Cánovas, María J.; Dinh, Nguyen; Long, Dang H.; Parra, Juan
• Is Part Of: Optimization. Volume 70:Number 8(2021)
• Page Start: 1637
• Page End: 1672
• Publication Date: 2021-08-03
• Subjects: Functional inequalities -- stable Farkas lemma -- qualification conditions -- composite vector functions -- composite vector optimization problems; 90C29 -- 90C46 -- 49N15 -- 90C48; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1745796
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : This paper generalizes and unifies different recent results as well as provides a new methodology concerning vector optimization problems involving composite mappings in locally convex Hausdorff topological vector spaces. The Lagrangian and weak Lagrangian dual problems are proposed. Characterizations of strong duality results are proved at the same time with characterizations of Farkas lemmas for composite vector mappings in a general setting (i.e. without any assumptions on convexity or continuity of the mappings involved). Corresponding results in the convex setting are also proposed by establishing as main tools some variants of representations of epigraphs of conjugate mappings in our composite vector framework. As by-products, several Farkas-type results for composite vector functions are proposed, which extend and cover several known ones recently appeared in the literature. Lastly, the results are applied to get duality results for a class of convex semi-vector bilevel optimization problems.