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  • Constrained polynomial optimization problems with noncommuting variables
    Cafuta, Kristijan, 1977- ; Klep, Igor, 1978- ; Povh, Janez, 1973-
    In this paper we study constrained eigenvalue optimization of noncommutative (nc) polynomials, focusing on the polydisc and the ball. Our three main results are as follows: (1) an nc polynomial is ... nonnegative if and only if it admits a weighted sum of hermitian squares decomposition; (2) (eigenvalue) optima for nc polynomials can be computed using a single semidefinite program (SDP) - this sharply contrasts with the commutative case where sequences of SDPs are needed; (3) the dual solution to this "single" SDP can be exploited to extract eigenvalue optimizers with an algorithm based on two ingredients: solution to a truncated nc moment problem via flat extensions, and Gelfand-Naimark-Segal construction. The implementation of these procedures in our computer algebra system NCSOStools is presented, and several examples pertaining to matrix inequalities are given to illustrate our results.
    Vir: SIAM journal on optimization. - ISSN 1052-6234 (Vol. 22, no. 2, 2012, str. 363-383)
    Vrsta gradiva - članek, sestavni del
    Leto - 2012
    Jezik - angleški
    COBISS.SI-ID - 16276569
vir: SIAM journal on optimization. - ISSN 1052-6234 (Vol. 22, no. 2, 2012, str. 363-383)
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