## Convergence rates of moment-sum-of-squares hierarchies for volume approximation of semialgebraic sets

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 … Read more

## SPECTRA – a Maple library for solving linear matrix inequalities in exact arithmetic

This document briefly describes our freely distributed Maple library {\sc spectra}, for Semidefinite Programming solved Exactly with Computational Tools of Real Algebra. It solves linear matrix inequalities in exact arithmetic and it is targeted to small-size, possibly degenerate problems for which symbolic infeasibility or feasibility certificates are required. Article Download View SPECTRA – a Maple … Read more

## Convergence rates of moment-sum-of-squares hierarchies for optimal control problems

We study the convergence rate of moment-sum-of-squares hierarchies of semidefinite programs for optimal control problems with polynomial data. It is known that these hierarchies generate polynomial under-approximations to the value function of the optimal control problem and that these under-approximations converge in the \$L^1\$ norm to the value function as their degree \$d\$ tends to … Read more