Analytical solutions of a class of matrix function optimization problems with unitary constraints. (January 2022) - Shen, Weijie; Shi, Ping; Ge, Zhihao; Xu, Weiwei
Abstract: In this paper we extend Theorems 3.1 and 3.2 of Xu et al. (2020) to more general cases and propose analytic solutions of the following constrained matrix maximization problems with unitary constraints: max S k S k H = I n, L k L k H = I m det c I m + ∏ k = 1 s A k S k B k L k and max S k S k H = I n, L k L k H = I m tr c I m + ∏ k = 1 s A k S k B k L k, where c is a complex number, I m denotes the m -order identity matrix, A k, B k are m × n and n × m complex matrices, and det ( ⋅ ), tr ( ⋅ ) denote the matrix determinant and trace functions. This is a non-convex nonlinear constrained matrix maximization problem. The new results improve the corresponding existing ones in Xu et al. (2020).