116 citations · 1.1k across the 72 of their papers we have counts for
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Semidefinite programming in matrix unknowns which are dimension free
J. William Helton, Igor Klep, Scott McCullough
One of the main applications of semidefinite programming lies in linear systems and control theory. Many problems in this subject, certainly the textbook classics, have matrices as…
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…
A local-global principle for linear dependence of noncommutative polynomials
Matej Bresar, Igor Klep
A set of polynomials in noncommuting variables is called locally linearly dependent if their evaluations at tuples of matrices are always linearly dependent. By a theorem of Camino…
The convex Positivstellensatz in a free algebra
J. William Helton, Igor Klep, Scott McCullough
Given a monic linear pencil L in g variables let D_L be its positivity domain, i.e., the set of all g-tuples X of symmetric matrices of all sizes making L(X) positive semidefinite.…