English

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).

Keywords

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}
}