A Solution Method for Generalized Semi-Infinite Programming ^{1}

S. J. Li, ^{2} S. Y. Wu, ^{3} K. L. Teo and X. Q. Yang ^{4}

May 13, 2002

Abstract: By using the idea of the discretization method in conjunction with the pattern search method, we derive an algorithm for generalized semi-infinite programming problems. We show that the sequence of points generated by the algorithm is a convergent sequence, and its accumulation point satisfies a Fritz-John optimality condition. For illustration, several numerical examples are solved by using the algorithm proposed. Keywords: Generalized semi-infinite programming, discretization method, pattern method.

1This research is partially supported by the Research Committee of The Hong Kong Polytechnic University, Research Grant committee of The Hong Kong and the National Natural Science Foundation of China.

2Department of Mathematics and Applied Mathematics, College of Sciences, Chongqing University (Campus B), Chongqing, 400045, China. E-mail: 00900470r@polyu.edu.hk. Current address: Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong

3Institute of Applied Mathematics, National Cheng-Kung University, Tainan 700, Taiwan Email:soonyi@mail.ncku.edu.tw

4Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong E-mail: mateokl@polyu.edu.hk and mayangxq@polyu.edu.hk.