Second-order cone and semidefinite methods for the bisymmetric matrix approximation problem

Abstract

Approximating the closest positive semi-definite bisymmetric matrix using the Frobenius norm to a data matrix is important in many engineering applications, communication theory and quantum physics. In this paper, we will use the interior point method to solve this problem. The problem will be reformulated into various forms, in the beginning as a semi-definite programming problem and later, into the form of a mixed semidefintie and second-order cone optimization problem. Numerical results comparing the efficiency of these methods with the alternating projection algorithm will be reported.