Mohab Safey El Din – Optimization Online

Convergence rate of the moment-SOS hierarchy for univariate polynomial optimization

Published: 2026/09/02

We study the convergence rate of the moment-SOS (sum-of-squares) hierarchy for polynomial optimization problems (POPs) on a bounded subset of the real line described by arbitrary polynomial inequalities. We prove that, for every fixed univariate POP, the relaxation error is bounded by $O(1/r^2)$, where $r$ is the relaxation order. In particular, boundary degeneracies in the … Read more

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

Published: 2016/11/05

Semi-definite Programming computer algebra, linear matrix inequalities, low-rank matrices, polynomial sums of squares, semidefinite programming

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. ArticleDownload View PDF