Paper Info
Title
Optimality Conditions for Convex Semi-infinite Programming Problems with Finitely Representable Compact Index Sets.
Abstract
In the present paper, we analyze a class of convex semi-infinite programming problems with arbitrary index sets defined by a finite number of nonlinear inequalities. The analysis is carried out by employing the constructive approach, which, in turn, relies on the notions of immobile indices and their immobility orders. Our previous work showcasing this approach includes a number of papers dealing with simpler cases of semi-infinite problems than the ones under consideration here. Key findings of the paper include the formulation and the proof of implicit and explicit optimality conditions under assumptions, which are less restrictive than the constraint qualifications traditionally used. In this perspective, the optimality conditions in question are also compared to those provided in the relevant literature. Finally, the way to formulate the obtained optimality conditions is demonstrated by applying the results of the paper to some special cases of the convex semi-infinite problems.
Year
DOI
Venue
2017
10.1007/s10957-017-1150-z
J. Optimization Theory and Applications
Keywords
Field
DocType
Convex programming,Semi-infinite programming (SIP),Nonlinear programming (NLP),Convex set,Finitely representable set,Constraint qualifications (CQ),Immobile index,Optimality conditions,90C25,90C30,90C34
Mathematical optimization,Constructive,Semi-infinite programming,Index set,Nonlinear programming,Convex set,Subderivative,Convex optimization,Convex analysis,Mathematics
Journal
Volume
Issue
ISSN
175
1
0022-3239
Citations 
PageRank 
References 
1
0.37
12
Authors
2
Name
Order
Citations
PageRank
Olga Kostyukova1124.47
T. V. Tchemisova211.38