The Optimization on Ranks and Inertias of a Quadratic Hermitian Matrix Function and Its Applications - Yirong Yao (Journal of Applied Mathematics)
We solve optimization problems on the ranks and inertias of the quadratic Hermitian matrix function subject to a consistent system of matrix equations and . As applications, we derive necessary and sufficient conditions for the solvability to the systems of matrix equations and matrix inequalities , and in the Löwner partial ordering to be feasible, respectively. The findings of this paper widely extend the known results in the literature.