Solving optimization problems on ranks and inertias of some constrained nonlinear matrix functions via an algebraic linearization method

We establish in this paper a group of closed-form formulas for calculating the global maximum and minimum ranks and inertias of the quadratic Hermitian matrix function ϕ ( X ) = Q − X P X ∗ with respect to the variable matrix X by using a linearization method and some known formulas for extremum ran...

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Bibliographic Details
Published in:	Nonlinear analysis Vol. 75; no. 2; pp. 717 - 734
Main Author:	Tian, Yongge
Format:	Journal Article
Language:	English
Published:	Amsterdam Elsevier Ltd 2012 Elsevier
Subjects:	Algebra Calculus of variations and optimal control Exact sciences and technology Finite differences and functional equations Generalized inverse Inertia Linear and multilinear algebra, matrix theory Linear matrix function Linearization method Löwner partial ordering Mathematical analysis Mathematics Matrices Matrix equation Matrix inequality Nonlinear algebraic and transcendental equations Nonlinearity Numerical analysis Numerical analysis. Scientific computation Optimization Order disorder Quadratic matrix function Rank Sciences and techniques of general use 65K15 Löwner partial ordering Rank Matrix inequality 15B57 15A09 Generalized inverse Linearization method Optimization 15A63 15A24 15B10 65K10 Inertia Quadratic matrix function Linear matrix function Matrix equation Optimization method Partial ordering Lowner partial ordering Mathematical model Linearization Nonlinear analysis Matrix function Algebraic method Problem solving
ISSN:	0362-546X, 1873-5215
Online Access:	Get full text
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