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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.

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
Full Text: DOI
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