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Estimating Maximum by Moments for Functions on Orbits

Alexander Barvinok
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Abstract

Let G be a compact group acting in a real vector space V. We obtain a number of inequalities relating the L^infinity norm of a matrix element of the representation of G with its L^p norm for p<infinity. We apply our results to obtain approximation algorithms to find the maximum absolute value of a given multivariate polynomial over the unit sphere (in which case G is the orthogonal group) and for the multidimensional assignment problem, a hard problem of combinatorial optimization (in which case G is the symmetric group).

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Alexander Barvinok. 2002-01-03. Estimating Maximum by Moments for Functions on Orbits. https://arxiv.org/abs/math/0201020

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