- Title
- Necessary and sufficient optimality conditions in DC semi-infinite programming
- Creator
- Correa, Rafael; López, Marco; Pérez-Aros, Pedro
- Date
- 2021
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/176607
- Identifier
- vital:15142
- Identifier
-
https://doi.org/10.1137/19M1303320
- Identifier
- ISBN:1052-6234 (ISSN)
- Abstract
- This paper deals with particular families of DC optimization problems involving suprema of convex functions. We show that the specific structure of this type of function allows us to cover a variety of problems in nonconvex programming. Necessary and sufficient optimality conditions for these families of DC optimization problems are established, where some of these structural features are conveniently exploited. More precisely, we derive necessary and sufficient conditions for (global and local) optimality in DC semi-infinite programming and DC cone-constrained optimization, under natural constraint qualifications. Finally, a penalty approach to DC abstract programming problems is developed in the last section. © 2021 Society for Industrial and Applied Mathematics
- Publisher
- Society for Industrial and Applied Mathematics Publications
- Relation
- SIAM Journal on Optimization Vol. 31, no. 1 (2021), p. 837-865
- Rights
- All metadata describing materials held in, or linked to, the repository is freely available under a CC0 licence
- Rights
- Copyright © 2021 Society for Industrial and Applied Mathematics
- Rights
- Open Access
- Subject
- 0102 Applied Mathematics; 0103 Numerical and Computational Mathematics; Cone-constraint programming; DC functions; Semi-infinite programming; Supremum function
- Full Text
- Reviewed
- Funder
- The first author was partially supported by ANID Chile under grant Fondecyt Regular 1190110. The second author is supported by Research Project PGC2018-097960-B-C21 from MICINN Spain, and Australian ARC–Discovery Projects DP 180100602. The third author was partially supported by ANID Chile under grants Fondecyt regular 1190110, Fondecyt regular 1200283, and Programa Regional Mathamsud 20-Math-08 CODE: MATH190003. †Universidad de O’Higgins, Rancagua, Chile and DIM-CMM of Universidad de Chile, Santiago, Chile (rafael.correa@uoh.cl). ‡Department of Mathematics, University of Alicante, Alicante 03080, Spain, and CIAO, Federation University, Australia (marco.antonio@ua.es). §Instituto de Ciencias de la Ingeniería, Universidad de O’Higgins, Rancagua 2820000, Chile (pedro.perez@uoh.cl).
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