116 citations · 258 across the 22 of their papers we have counts for
5 papers · 1 filter
Spectrahedral relaxations of hyperbolicity cones
Markus Schweighofer
Let be a real zero polynomial in variables. Then defines a rigidly convex set . We construct a linear matrix inequality of size in the same variables th…
An exact duality theory for semidefinite programming based on sums of squares
Igor Klep, Markus Schweighofer
Farkas' lemma is a fundamental result from linear programming providing linear certificates for infeasibility of systems of linear inequalities. In semidefinite programming, such l…
Infeasibility certificates for linear matrix inequalities
Igor Klep, Markus Schweighofer
Farkas' lemma is a fundamental result from linear programming providing linear certificates for infeasibility of systems of linear inequalities. In semidefinite programming, such l…
Exposed faces of semidefinitely representable sets
Tim Netzer, Daniel Plaumann, Markus Schweighofer
A linear matrix inequality (LMI) is a condition stating that a symmetric matrix whose entries are affine linear combinations of variables is positive semidefinite. Motivated by the…
A note on the representation of positive polynomials with structured sparsity
David Grimm, Tim Netzer, Markus Schweighofer
We consider real polynomials in finitely many variables. Let the variables consist of finitely many blocks that are allowed to overlap in a certain way. Let the solution set of a f…