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Polyhedra, spectrahedra and the question of containment

Polyhedra (or in the bounded cases polytopes) are the feasible regions of linear programs. Generalizing this notion, spectrahedra are defined as the feasible regions of semidefinite programs. In this talk, we first provide some general insights into the emerging world of spectrahedra. Then we study the computational question whether a given polytope or spectrahedron S_A (as given by the positive semidefiniteness region of a linear matrix pencil A(x)) is contained in another one S_B.

(Joint work with Kai Kellner and Christian Trabandt.)


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