Optimality Conditions in DC-Constrained Mathematical Programming Problems

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...

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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 198; no. 3; pp. 1191 - 1225
Main Authors: Correa, Rafael, López, Marco A., Pérez-Aros, Pedro
Format: Journal Article
Language:English
Published: New York Springer US 01.09.2023
Springer Nature B.V
Subjects:
Applications of Mathematics
Applied mathematics
Calculus of Variations and Optimal Control; Optimization
Convex analysis
Engineering
Mathematical analysis
Mathematical programming
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Semidefinite programming
Theory of Computation
90C34
Supremum function
90C26
DC-constrained programming
Infinite programming
DC functions
Conic programming
Semi-definite programming
Stochastic programming
Primary: 90C30
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Summary: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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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-023-02260-x