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Zbl 1236.65070
Tian, Yongge
Solving optimization problems on ranks and inertias of some constrained nonlinear matrix functions via an algebraic linearization method.
(English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 75, No. 2, 717-734 (2012). ISSN 0362-546X

The author considers a group of closed-form formulas for calculating the global maximum and minimum ranks and inertias of the quadratic Hermitian matrix function $\phi(X)= Q- XPX^*$ with respect to the variable matrix $X$ by using a linearization method and some known formulas for extremum ranks and inertias of linear Hermitian matrix functions, where both $P$ and $Q$ are complex Hermitian matrices and $X^*$ is the conjugate transpose of $X$.\par Examples are presented to illustrative applications of the equality-constrained quadratic optimization in some matrix completion problems.
[Hans Benker (Merseburg)]
MSC 2000:
*65K05 Mathematical programming (numerical methods)
15A09 Matrix inversion
15A24 Matrix equations
15A63 Bilinear forms, etc.
15B10
15B57

Keywords: linear matrix function; quadratic matrix function; rank; inertia; Löwner partial ordering; generalized inverse; matrix equation; matrix inequality; optimization; linearization method

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