A relaxed cutting plane method for semi-infinite semi-definite programming

Authors:
S. J. Li;S. Y. Wu;X. Q. Yang;K. L. Teo
Affiliations:
Department of Information and Computer Sciences, College of Sciences, Chongqing University, Chongqing, China;Institute of Applied Mathematics, National Cheng-Kung University, Tainan, Taiwan;Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong;Department of Mathematics and Statistics, Curtin University of Technology, Perth, Australia
Venue:
Journal of Computational and Applied Mathematics
Year:
2006

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Abstract

In this paper, we develop two discretization algorithms with a cutting plane scheme for solving combined semi-infinite and semi-definite programming problems, i.e., a general algorithm when the parameter set is a compact set and a typical algorithm when the parameter set is a box set in the m-dimensional space. We prove that the accumulation point of the sequence points generated by the two algorithms is an optimal solution of the combined semi-infinite and semi-definite programming problem under suitable assumption conditions. Two examples are given to illustrate the effectiveness of the typical algorithm.