Optimality conditions in DC constrained mathematical programming problems

2022/07/28 by Rafael Corrêa, Correa, Rafael, Marco A. López +3
Computer Science · Economics, Econometrics and Finance · Engineering · #90C26 #90C30 #90C34 #Economic theories and models #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Mathematical Programming #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2207.14059

openalex publication_date 2022/07/28 · openalex created_date 2022/07/30 · openalex updated_date 2026/07/28

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.

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