Conjugate cone characterization of positive definite and semidefinite matrices

DOI10.1016/0024-3795(84)90116-2zbMath0529.15013OpenAlexW2071210172MaRDI QIDQ787230

Olvi L. Mangasarian, Shih-Ping Han

Publication date: 1984

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: http://digital.library.wisc.edu/1793/58380

zbMATH Keywords

closed convex coneslocal duality resultsMoreau's polar decompositionpositive definite and semidefinite matrices

Mathematics Subject Classification ID

Positive matrices and their generalizations; cones of matrices (15B48) Hermitian, skew-Hermitian, and related matrices (15B57)

Related Items (12)

Relative eigenvalues of Hermitian matrices ⋮ On inertia and Schur complement in optimization ⋮ Radial wavelet transform on Iwasawa subgroups ⋮ Moreau's decomposition in Banach spaces ⋮ Think co(mpletely)positive! Matrix properties, examples and a clustered bibliography on copositive optimization ⋮ The inverse of a symmetric nonnegative matrix can be copositive ⋮ A fresh variational-analysis look at the positive semidefinite matrices world ⋮ Characterization of Positive Definite and Semide Finite Matrices via Quadratic Programming Duality ⋮ On the generalized inverse of a copositive matrix ⋮ A characterization of positive-semidefinite operators on a Hilbert space ⋮ Cone characterizations of positive semidefinite operators on a Hilbert space ⋮ An inertia theorem for symmetric matrices and its application to nonlinear programming

Cites Work

• Complementary pivot theory of mathematical programming
• Local Duality of Nonlinear Programs
• Discrete Splines via Mathematical Programming
• On Quadratic Programming
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