- Convergence rates of moment-sum-of-squares hierarchies for volume approximation of semialgebraic sets Milan Korda(milan.kordaengineering.ucsb.edu) Didier Henrion(henrionlaas.fr) Abstract: Moment-sum-of-squares hierarchies of semidefinite programs can be used to approximate the volume of a given compact basic semialgebraic set \$K\$. The idea consists of approximating from above the indicator function of \$K\$ with a sequence of polynomials of increasing degree \$d\$, so that the integrals of these polynomials generate a convergence sequence of upper bounds on the volume of \$K\$. We show that the asymptotic rate of this convergence is at least \$O(1 / \log \log d)\$. Keywords: moment relaxations, polynomial sums of squares, convergence rate, semidefinite programming, approximation theory Category 1: Linear, Cone and Semidefinite Programming (Semi-definite Programming ) Category 2: Infinite Dimensional Optimization (Other ) Citation: Download: [PDF]Entry Submitted: 12/12/2016Entry Accepted: 12/13/2016Entry Last Modified: 12/12/2016Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.