A smoothing Levenberg–Marquardt algorithm for semi-infinite programming

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• 作者：Ping Jin ; Chen Ling ; Huifei Shen
• 关键词：Semi ; infinite programming (SIP) problem ; KKT system ; Nonsmooth equations ; Smoothing Levenberg–Marquardt algorithm ; Convergence ; 49M15 ; 49M37 ; 65K15 ; 90C30 ; 90C46
• 刊名：Computational Optimization and Applications
• 出版年：2015
• 出版时间：April 2015
• 年：2015
• 卷：60
• 期：3
• 页码：675-695
• 全文大小：288 KB
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Optimization
  Operations Research and Mathematical Programming
  Operation Research and Decision Theory
  Statistics
  Convex and Discrete Geometry
  
• 出版者：Springer Netherlands
• ISSN：1573-2894

文摘

In this paper, we present a smoothing Levenberg–Marquardt algorithm for the solution of the semi-infinite programming (SIP) problem. We first reformulate the KKT system of SIP problem into a system of constrained nonsmooth equations. Then we solve this system by a smoothing Levenberg–Marquardt algorithm. The feasibility is ensured via the aggregated constraint, and at each iteration of the presented algorithm only a quadratic programming has to be solved. Global and local superlinear convergence of this algorithm is established under a local error bound condition, which is much weaker than the nonsingularity condition. Preliminary numerical results are reported.