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.
Original language | English |
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Pages (from-to) | 459-473 |
Number of pages | 15 |
Journal | Journal of Computational and Applied Mathematics |
Volume | 196 |
Issue number | 2 |
DOIs | |
Publication status | Published - 15 Nov 2006 |
Keywords
- Cutting plane scheme
- Discretization algorithm
- Semi-infinite and semi-definite program
ASJC Scopus subject areas
- Applied Mathematics
- Computational Mathematics
- Numerical Analysis