An extended conjugate duality for generalized semi-infinite programming problems via a convex decomposition. (2nd August 2020)

• Record Type: Journal Article
• Authors: Aboussoror, A.; Adly, S.; Salim, S.
• Is Part Of: Optimization. Volume 69:Number 7/8(2020)
• Page Start: 1635
• Page End: 1654
• Publication Date: 2020-08-02
• Subjects: Generalized semi-infinite programming -- reverse convex problems -- DC problems -- convex analysis -- conjugate duality; 90C34 -- 90C26 -- 46N10 -- 90C46; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1655739
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: We present an extended conjugate duality for a generalized semi-infinite programming problem ( P ) . The extended duality is defined in the context of the absence of convexity of problem ( P ), by means of a decomposition into a family of convex subproblems and a conjugate dualization of the subproblems. Under appropriate assumptions, we establish strong extended duality and provide necessary and sufficient optimality conditions for problem ( P ) . These extended conjugate duality and optimality conditions are new in the literature of generalized semi-infinite programming.