منابع مشابه
Deciding Polyhedrality of Spectrahedra
Spectrahedra are linear sections of the cone of positive semidefinite matrices which, as convex bodies, generalize the class of polyhedra. In this paper we investigate the problem of recognizing when a spectrahedron is polyhedral. We generalize and strengthen results of [M. V. Ramana, Polyhedra, spectrahedra, and semidefinite programming, in Topics in Semidefinite and Interior-Point Methods, Fi...
متن کاملSpectrahedra and Their Shadows
eingereichte Habilitationsschrift zur Erlangung des akademischen Grades doctor rerum naturalium habilitatus Die Annahme der Habilitationsschrift haben empfohlen:
متن کاملPolyhedra, Spectrahedra, and Semideenite Programming
A spectrahedron is the feasible region of a semideenite program. In this paper, we investigate the conditions under which a given spectrahedron is polyhedral. Characterizations of those matrix maps for which the associated spectrahedron is polyhedral are derived. It is then shown that, while polyhedrality is CoNP-Hard to detect in general, under certain assumptions, it can be recognized in rand...
متن کاملA Semidefinite Hierarchy for Containment of Spectrahedra
A spectrahedron is the positivity region of a linear matrix pencil and thus the feasible set of a semidefinite program. We propose and study a hierarchy of sufficient semidefinite conditions to certify the containment of a spectrahedron in another one. This approach comes from applying a moment relaxation to a suitable polynomial optimization formulation. The hierarchical criterion is stronger ...
متن کاملContainment Problems for Polytopes and Spectrahedra
We study the computational question whether a given polytope or spectrahedron SA (as given by the positive semidefiniteness region of a linear matrix pencil A(x)) is contained in another one SB . First we classify the computational complexity, extending results on the polytope/polytope-case by Gritzmann and Klee to the polytope/spectrahedron-case. For various restricted containment problems, NP...
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ژورنال
عنوان ژورنال: Mathematical Programming
سال: 2014
ISSN: 0025-5610,1436-4646
DOI: 10.1007/s10107-014-0844-3