sum of hermitian squares – Optimization Online

NCSOSTOOLS: A COMPUTER ALGEBRA SYSTEM FOR SYMBOLIC AND NUMERICAL COMPUTATION WITH NONCOMMUTATIVE POLYNOMIALS

Published: 2010/05/30, Updated: 2012/03/01

Optimization Software and Modeling Systems, Semi-definite Programming commutator, noncommutative polynomial, semidefi, sum of hermitian squares

Abstract. NCSOStools is a Matlab toolbox for – symbolic computation with polynomials in noncommuting variables; – constructing and solving sum of hermitian squares (with commutators) programs for polynomials in noncommuting variables. It can be used in combination with semidefinite programming software, such as SeDuMi, SDPA or SDPT3 to solve these constructed programs. This paper provides … Read more

On the nonexistence of sum of squares certificates for the BMV conjecture

Published: 2009/10/27, Updated: 2011/03/21

Kristijan Cafuta

Igor Klep

Janez Povh

Basic Sciences Applications, Semi-definite Programming bessis-moussa-villani (bmv) conjecture, commutator, cyclic equivalence, noncommutative polynomial, semidefinite programming, sum of hermitian squares

The algebraic reformulation of the BMV conjecture is equivalent to a family of dimensionfree tracial inequalities involving positive semidefinite matrices. Sufficient conditions for these to hold in the form of algebraic identities involving polynomials in noncommuting variables have been given by Markus Schweighofer and the second author. Later the existence of these certificates has been … Read more