- Max-min optimizations on the rank and inertia of a linear Hermitian matrix expression subject to range, rank and definiteness restrictions Yongge Tian(yongge.tiangmail.com) Abstract: The inertia of a Hermitian matrix is defined to be a triplet composed by the numbers of the positive, negative and zero eigenvalues of the matrix counted with multiplicities, respectively. In this paper, we give various closed-form formulas for the maximal and minimal values for the rank and inertia of the Hermitian expression $A + X$, where $A$ is a given Hermitian matrix and $X$ is a variable Hermitian matrix satisfying the range and rank restrictions ${\rm range}(X) \subseteq {\rm range}(B)$ and ${\rm rank}(X) \leqslant k$. Some expressions of the Hermitian matrix $X$ such that $A + X$ attains the extremal ranks and inertias are also presented. Keywords: Hermitian matrix expression; perturbation; rank; inertia; maximization; minimization; Moore--Penrose inverse; equality; inequality Category 1: Global Optimization Category 2: Global Optimization (Theory ) Citation: Download: [PDF]Entry Submitted: 10/28/2010Entry Accepted: 10/29/2010Entry Last Modified: 10/28/2010Modify/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 Optimization Online is supported by the Mathematical Programming Society.