5 citations · 9 across the 5 of their papers we have counts for
6 papers
Irreducible infeasible subsystems of semidefinite systems
Kai Kellner, Marc E. Pfetsch, Thorsten Theobald
Farkas' lemma for semidefinite programming characterizes semidefinite feasibility of linear matrix pencils in terms of an alternative spectrahedron. In the well-studied special cas…
A Semidefinite Hierarchy for Disjointly Constrained Multilinear Programming
Kai Kellner
Disjointly constrained multilinear programming concerns the problem of maximizing a multilinear function on the product of finitely many disjoint polyhedra. While maximizing a line…
Containment Problems for Projections of Polyhedra and Spectrahedra
Kai Kellner
Spectrahedra are affine sections of the cone of positive semidefinite matrices which form a rich class of convex bodies that properly contains that of polyhedra. While the class of…
Sum of Squares Certificates for Containment of -polytopes in -polytopes
Kai Kellner, Thorsten Theobald
Given an -polytope and a -polytope , the decision problem whether is contained in is co-NP-complete. This hardness remains if is restri…
A Semidefinite Hierarchy for Containment of Spectrahedra
Kai Kellner, Thorsten Theobald, Christian Trabandt
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…
Containment problems for polytopes and spectrahedra
Kai Kellner, Thorsten Theobald, Christian Trabandt
We study the computational question whether a given polytope or spectrahedron (as given by the positive semidefiniteness region of a linear matrix pencil ) is contained…