Paper Info
Title
A Regularized Explicit Exchange Method for Semi-Infinite Programs with an Infinite Number of Conic Constraints.
Abstract
The semi-infinite program (SIP) is normally represented with infinitely many inequality constraints and has been studied extensively so far. However, there have been very few studies on the SIP involving conic constraints, even though it has important applications such as Chebyshev-like approximation, filter design, and so on. In this paper, we focus on the SIP with infinitely many conic constraints, called an SICP for short. We show that under the Robinson constraint qualification a local optimum of the SICP satisfies the KKT conditions that can be represented only with a finite subset of the conic constraints. We also introduce two exchange type algorithms for solving the convex SICP. We first provide an explicit exchange method and show that it has global convergence under the strict convexity assumption on the objective function. We then propose an algorithm combining a regularization method with the explicit exchange method and establish global convergence of the hybrid algorithm without the strict convexity assumption. We report some numerical results to examine the effectiveness of the proposed algorithms.
Year
DOI
Venue
2012
10.1137/110839631
SIAM JOURNAL ON OPTIMIZATION
Keywords
Field
DocType
semi-infinite programming,conic constraints,exchange method
Convergence (routing),Discrete mathematics,Convexity,Mathematical optimization,Hybrid algorithm,Semi-infinite,Local optimum,Semi-infinite programming,Karush–Kuhn–Tucker conditions,Conic section,Mathematics
Journal
Volume
Issue
ISSN
22
3
1052-6234
Citations 
PageRank 
References 
4
0.45
7
Authors
3
Name
Order
Citations
PageRank
Takayuki Okuno140.45
Shunsuke Hayashi2865.31
Masao Fukushima32050172.73