Solutions to optimization problems on ranks and inertias of a matrix function with applications

• Published in: Applied mathematics and computation Vol. 219; no. 6; pp. 2989 - 3001
• Main Authors: He, Zhuo-Heng, Wang, Qing-Wen
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 25.11.2012
• Subjects: Computation; Conjugates; Inertia; Mathematical analysis; Mathematical models; Matrix equation; Moore–Penrose inverse; Optimization; Rank; Re-nonnegative semidefinite matrix; Rank; Inertia; Moore–Penrose inverse; Matrix equation; Re-nonnegative semidefinite matrix

Consider the Hermitian matrix function f(X)=A3-B3X-(B3X)∗ subject to a consistent system of matrix equations (0.1)A1X=C1,A2XB2=C2,where ∗ means conjugate transpose. In this paper we first establish explicit expansion formulas to calculate the global maximal and minimal ranks and inertias of the Herm...