Estimating Maximum by Moments for Functions on Orbits
Optimization and Control
2007-05-23 v1 Combinatorics
Representation Theory
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).
Cite
@article{arxiv.math/0201020,
title = {Estimating Maximum by Moments for Functions on Orbits},
author = {Alexander Barvinok},
journal= {arXiv preprint arXiv:math/0201020},
year = {2007}
}