An extended conjugate duality for generalized semi-infinite programming problems via a convex decomposition

ABSTRACT

We present an extended conjugate duality for a generalized semi-infinite programming problem $\left(\mathcal{P}\right)$. The extended duality is defined in the context of the absence of convexity of problem $\left(\mathcal{P}\right)$, 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 $\left(\mathcal{P}\right)$. These extended conjugate duality and optimality conditions are new in the literature of generalized semi-infinite programming.

KEYWORDS:

• Generalized semi-infinite programming
• reverse convex problems
• DC problems
• convex analysis
• conjugate duality

AMS SUBJECT CLASSIFICATIONS:

• 90C34
• 90C26
• 46N10
• 90C46

Disclosure statement

No potential conflict of interest was reported by the authors.