Riemannian Trust-Region Method for the Log-Determinant Model of Hermitian Matrix Eigenproblems

The logarithm of the determinant of Hermitian positive semi-definite matrices arises in numerous contexts in statistic, machine learning, and information and communication engineering. In this paper, based on the logarithm of determinant, we propose the log-determinant optimization model from the Riemannian optimization viewpoint to compute the dominant eigenvalues and associated eigenvectors of a Hermitian positive semi-definite matrix. The Riemannian trust-region method is employed to solve this optimization problem. Experimental results are reported to show the efficiency of the proposed method.