An extension of analytic solutions of a class of constrained matrix minimization problems

Abstract

In this paper we consider an extension of analytic solutions of a class of constrained matrix minimization problems and propose analytic solutions of the following matrix minimization problem: minSkSkH=In,LkLkH=Im|det(cIm±∏k=1sAkSkBkLk)|minSkSkH=In,LkLkH=Im|tr(cIm±∏k=1sAkSkBkLk)|,where Ak∈Cm×n,Bk∈Cn×m,c is a complex number, Im denotes m-order identity matrix, and det(⋅),tr(⋅) denote matrix determinant and trace function. The proposed results improve the corresponding existing ones in Xu et al. (2019). Numerical examples are provided to illustrate the efficiency of the proposed theoretical results.