ANZIAM J.
45 (2004), 477494

A solution method for combined semiinfinite and semidefinite programming

S. J. Li
Department of Information and Computer Sciences
College of Sciences
Chongqing University
Chongqing 400044
China
lisj@cqu.edu.cn


X. Q. Yang
Department of Applied Mathematics
The Hong Kong Polytechnic University
Kowloon
Hong Kong
mayangxq@polyu.edu.hk


K. L. Teo
Department of Applied Mathematics
The Hong Kong Polytechnic University
Kowloon
Hong Kong
mateokl@polyu.edu.hk




Abstract

In this paper, we develop a discretisation
algorithm with an adaptive scheme for solving a
class of combined semiinfinite and semidefinite
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 semiinfinite and semidefinite
programming problem. To illustrate the
effectiveness of the algorithm, two specific
classes of problems are solved. They are
relaxations of quadratically constrained
semiinfinite quadratic programming problems and
semiinfinite eigenvalue problems.

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