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Algorithmic aspects of sums of hermitian squares of noncommutative polynomials

Sabine Burgdorf (sabine.burgdorf***at***uni-konstanz.de)
Kristijan Cafuta (kristijan.cafuta***at***fe.uni-lj.si)
Igor Klep (igor.klep***at***fmf.uni-lj.si)
Janez Povh (janez.povh***at***fis.unm.si)

Abstract: This paper presents an algorithm and its implementation in the software package NCSOStools for finding sums of hermitian squares and commutators decompositions for polynomials in noncommuting variables. The algorithm is based on noncommutative analogs of the classical Gram matrix method and the Newton polytope method, which allows us to use semidefinite programming. Throughout the paper several examples are given illustrating the results.

Keywords: sum of squares, semidefinite programming, noncommutative polynomial, Matlab toolbox, Newton polytope, free positivity

Category 1: Global Optimization

Citation: Computational Optimization and Applications, 2013, vol. 55, iss. 1, pp. 137-153

Download: [PDF]

Entry Submitted: 11/21/2011
Entry Accepted: 12/01/2011
Entry Last Modified: 08/02/2013

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