ANZIAM J.
45 (2004), 477-494
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A solution method for combined semi-infinite and semi-definite programming
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S. J. Li
Department of Information
and Computer Sciences
College of Sciences
Chongqing University
Chongqing 400044
China
lisj@cqu.edu.cn
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X. Q. Yang
Department of Applied Mathematics
The Hong Kong Polytechnic University
Kowloon
Hong Kong
mayangxq@polyu.edu.hk
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K. L. Teo
Department of Applied Mathematics
The Hong Kong Polytechnic University
Kowloon
Hong Kong
mateokl@polyu.edu.hk
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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.
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