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

S. J. Li, S. Y. Wu, Xiaoqi Yang, K. L. Teo

Research output: Journal article publicationJournal articleAcademic researchpeer-review

1 Citation (Scopus)

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 languageEnglish
Pages (from-to)459-473
Number of pages15
JournalJournal of Computational and Applied Mathematics
Volume196
Issue number2
DOIs
Publication statusPublished - 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

Cite this