A relaxed cutting plane method for semi-infinite semi-definite programming |
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| Affiliation: | 1. Department of Information and Computer Sciences, College of Sciences, Chongqing University, Chongqing 400044, China;2. Institute of Applied Mathematics, National Cheng-Kung University, Tainan 700, Taiwan;3. Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong;4. Department of Mathematics and Statistics, Curtin University of Technology, GPO Box U1987, Perth, W.A. 6845, Australia |
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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. |
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