Robust Approximate Optimality Conditions for Uncertain Nonsmooth Optimization with Infinite Number of Constraints

This paper deals with robust quasi approximate optimal solutions for a nonsmooth semi-infinite optimization problems with uncertainty data. By virtue of the epigraphs of the conjugates of the constraint functions, we first introduce a robust type closed convex constraint qualification. Then, by usin...

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Bibliographic Details
Published inMathematics (Basel) Vol. 7; no. 1; p. 12
Main Authors Sun, Xiangkai, Fu, Hongyong, Zeng, Jing
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.01.2019
Subjects
approximate quasi-solutions
Convex analysis
Food science
Mathematical functions
Mathematical programming
optimality conditions
Optimization
Optimization techniques
robust nonsmooth semi-infinite optimization
Robustness (mathematics)
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Summary:This paper deals with robust quasi approximate optimal solutions for a nonsmooth semi-infinite optimization problems with uncertainty data. By virtue of the epigraphs of the conjugates of the constraint functions, we first introduce a robust type closed convex constraint qualification. Then, by using the robust type closed convex constraint qualification and robust optimization technique, we obtain some necessary and sufficient optimality conditions for robust quasi approximate optimal solution and exact optimal solution of this nonsmooth uncertain semi-infinite optimization problem. Moreover, the obtained results in this paper are applied to a nonsmooth uncertain optimization problem with cone constraints.
ISSN:2227-7390
2227-7390
DOI:10.3390/math7010012