On solving a class of linear semi-infinite programming by SDP method

Abstract

In this paper, we present a new method to solve linear semi-infinite programming. This method bases on the fact that the nonnegative polynomial on could be turned into a positive semi-definite system, so we can use the nonnegative polynomials to approximate the semi-infinite constraint. Furthermore, we set up an approximate programming for the primal linear semi-infinite programming, and obtain an error bound between two programming problems. Numerical results show that our method is efficient.

Keywords:

• semi-infinite programming
• nonnegative polynomial
• SOS method
• semi-definite programming
• error bound

AMS Subject Classifications:

• 90C34
• 90C22

Acknowledgments

This work was supported by the Research Grant Council of Hong Kong, the National Natural Science Foundation of China (grant No. 11071122, 11171159); the Specialized Research Fund of Doctoral Program of Higher Education of China (grant No. 20103207110002).