An Approximation Bound Analysis for Lasserre’s Relaxation in Multivariate Polynomial Optimization

Abstract

Suppose f(x), g1(x), . . . , gm(x) are multivariate polynomials in x ∈ Rn and their degrees are at most 2d. Consider the optimization problem min f(x) s.t. x ∈ S = {x ∈ R : g1(x) ≥ 0, . . . , gm(x) ≥ 0}. Let fmin (resp., fmax) be the minimum (resp., maximum) of f(x) on S, and fsos be the lower bound of fmin given by Lasserre’s relaxation of order d. This… (More)

Topics

2 Figures and Tables

Cite this paper

@inproceedings{Nie2011AnAB, title={An Approximation Bound Analysis for Lasserre’s Relaxation in Multivariate Polynomial Optimization}, author={Jiawang Nie}, year={2011} }