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Solutions of a constrained Hermitian matrix-valued function optimization problem with applications. (English) Zbl 1357.65079
The paper considers a group of problems on ranks/inertias, equalities/inequalities, minimization/maximization in the Löwner partial ordering of a Hermitian matrix-valued function subject to a linear matrix equation by using algebraic operations of the given matrices in the function and restriction. The author presents results in solving problems on Hermitian matrix-valued functions subject to linear matrix equation restrictions where the Lagrangian method is not available.

MSC:
65K05 Numerical mathematical programming methods
15A09 Theory of matrix inversion and generalized inverses
15A24 Matrix equations and identities
47A62 Equations involving linear operators, with operator unknowns
90C22 Semidefinite programming
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