  


Solutions of a constrained Hermitian matrixvalued function optimization problem with applications
Tian Yongge(yongge.tiangmail.com) Abstract: Let $f(X) =\left( XC + D\right)M\left(XC + D \right)^{*}  G$ be a given nonlinear Hermitian matrixvalued function with $M = M^*$ and $G = G^*$, and assume that the variable matrix $X$ satisfies the consistent linear matrix equation $XA = B$. This paper shows how to characterize the semidefiniteness of $f(X)$ subject to all solutions of $XA = B$. As applications, a standard method is obtained for finding analytical solutions $X_0$ of $X_0A = B$ such that the matrix inequality $f(X) \succcurlyeq f(X_0)$ or $f(X) \preccurlyeq f(X_0)$ holds for all solutions of $X\!A = B$. The whole work provides direct access, as a standard example, to a very simple algebraic treatment of the constrained Hermitian matrixvalued function and the corresponding semidefiniteness and optimization problems. Keywords: Hermitian matrixvalued function; rank, inertia, semidefiniteness; L\"owner partial ordering; optimization problem Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization ) Citation: Download: [PDF] Entry Submitted: 12/10/2015 Modify/Update this entry  
Visitors  Authors  More about us  Links  
Subscribe, Unsubscribe Digest Archive Search, Browse the Repository

Submit Update Policies 
Coordinator's Board Classification Scheme Credits Give us feedback 
Optimization Journals, Sites, Societies  