Optimality conditions in DC constrained mathematical programming problems

TL;DR

This paper establishes new necessary and sufficient optimality conditions for constrained mathematical programming problems in locally convex spaces, utilizing generalized differentiation and the structure of difference of convex functions.

Contribution

It introduces novel qualification conditions and extends optimality theory beyond Asplund spaces, with applications to various advanced programming problems.

Findings

Derived optimality conditions in locally convex spaces

Extended the applicability beyond Asplund spaces

Applied results to infinite, stochastic, and semi-definite programming

Abstract

This paper provides necessary and sufficient optimality conditions for abstract constrained mathematical programming problems in locally convex spaces under new qualification conditions. Our approach exploits the geometrical properties of certain mappings, in particular their structure as difference of convex functions, and uses techniques of generalized differentiation (subdifferential and coderivative). It turns out that these tools can be used fruitfully out of the scope of Asplund spaces. Applications to infinite, stochastic and semi-definite programming are developed in separate sections.