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A solution method for combined semi-infinite and semi-definite programming

Published online by Cambridge University Press:  17 February 2009

S. J. Li ,
X. Q. Yang ,
K. L. Teo  and
S. Y. Wu
S. J. Li
Affiliation:
Department of Information and Computer Sciences, College of Sciences, Chongqing University, Chongqing, 400044, China; e-mail: [email protected].
X. Q. Yang
Affiliation:
Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong; e-mail: [email protected] and [email protected].
K. L. Teo
Affiliation:
Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong; e-mail: [email protected] and [email protected].
S. Y. Wu
Affiliation:
Institute of Applied Mathematics, National Cheng-Kung University, Tainan 700, Taiwan; e-mail: [email protected].
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Abstract

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In this paper, we develop a discretisation algorithm with an adaptive scheme for solving a class of combined semi-infinite and semi-definite programming problems. We show that any sequence of points generated by the algorithm contains a convergent subsequence; and furthermore, each accumulation point is a local optimal solution of the combined semi-infinite and semi-definite programming problem. To illustrate the effectiveness of the algorithm, two specific classes of problems are solved. They are relaxations of quadratically constrained semi-infinite quadratic programming problems and semi-infinite eigenvalue problems.

Type
Research Article
Information
The ANZIAM Journal , Volume 45 , Issue 4 , April 2004 , pp. 477 - 494
Copyright
Copyright © Australian Mathematical Society 2004

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