Robust envelope-constrained filter with orthonormal bases and semi-definite and semi-infinite programming

In this paper, the equivalence relation between a semi-infinite quadratically constrained convex quadratic programming problem and a combined semidefinite and semi-infinite programming problem is considered. Then, an efficient and reliable discretization algorithm for solving a general class of combined semidefinite and semi-infinite programming problems is developed. Both the continuoustime envelope-constrained optimal equalization filter and the corresponding robust envelope-constrained filter for a communication channel are solved by using the proposed algorithm. This research was partially supported by the Research Committee of The Hong Kong Polytechnic University and the National Natural Science Foundation of China (Grant numbers: 60574073 and 10471142). S.J. Li ( ) College of Mathematics and Science, Chongqing University, Chongqing 400044, China e-mail: [email protected] K.L. Teo Department of Mathematics and Statistics, Curtin University of Technology, GPO Box U1987, Perth, WA 6845, Australia e-mail: [email protected] X.Q. Yang Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong e-mail: [email protected] S.Y. Wu Institute of Applied Mathematics, National Cheng-Kung University, Tainan 700, Taiwan e-mail: [email protected] S.Y. Wu National Center for Theoretical Sciences, Tainan 701, Taiwan