Constrained Polynomial Optimization Problems with Noncommuting Variables
نویسندگان
چکیده
منابع مشابه
Constrained Polynomial Optimization Problems with Noncommuting Variables
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 shar...
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Consider the algebra Q〈〈x1, x2, . . .〉〉 of formal power series in countably many noncommuting variables over the rationals. The subalgebra Π(x1, x2, . . .) of symmetric functions in noncommuting variables consists of all elements invariant under permutation of the variables and of bounded degree. We develop a theory of such functions analogous to the ordinary theory of symmetric functions. In p...
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ژورنال
عنوان ژورنال: SIAM Journal on Optimization
سال: 2012
ISSN: 1052-6234,1095-7189
DOI: 10.1137/110830733