A hybrid algorithm for solving minimization problem over (R,S)-symmetric matrices with the matrix inequality constraint

In this paper, we consider the following minimization problem:where , , , and are given. An efficient inequality relaxation technique is presented to relax the matrix inequality constraint so that there is an optimal solution which is (R,S)-symmetric that minimize , and also satisfies the corrected matrix inequality constraint. A hybrid algorithm with convergence analysis is given to solve this problem. Numerical examples show that the algorithm requires less CPU times when compared with some other methods.

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