Optimality Conditions in DC-Constrained Mathematical Programming Problems

Rafael Correa (), Marco A. López () and Pedro Pérez-Aros ()
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Rafael Correa: Universidad de O’Higgins
Marco A. López: University of Alicante
Pedro Pérez-Aros: Universidad de O’Higgins

Journal of Optimization Theory and Applications, 2023, vol. 198, issue 3, No 12, 1225 pages

Abstract: 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.

Keywords: DC functions; DC-constrained programming; Conic programming; Infinite programming; Stochastic programming; Semi-definite programming; Supremum function; Primary: 90C30; 90C34; 90C26 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10957-023-02260-x

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