This paper is concerned with polynomial optimization problems. We show how to exploit
term (or monomial) sparsity of the input polynomials to obtain a new converging hierarchy of …

This work proposes a new moment-SOS hierarchy, called CS-TSSOS, for solving large-
scale sparse polynomial optimization problems. Its novelty is to exploit simultaneously …

This work is a follow-up and a complement to [J. Wang, V. Magron and JB Lasserre, preprint,
arxiv: 1912.08899, 2019] where the TSSOS hierarchy was proposed for solving polynomial …

In this expository article, we study optimization problems specified via linear and relative
entropy inequalities. Such relative entropy programs (REPs) are convex optimization …

We describe a generalization of the Sums-of-AM/GM-Exponential (SAGE) methodology for
relative entropy relaxations of constrained signomial and polynomial optimization problems …

Recently, the second and third authors developed sums of nonnegative circuit polynomials
(SONC) as a new certificate of nonnegativity for real polynomials, which is independent of …

This article studies the parameter tuning problem of positive linear systems for optimizing
their stability properties. We specifically show that, under certain regularity assumptions on …

Certifying function nonnegativity is a ubiquitous problem in computational mathematics, with
especially notable applications in optimization. We study the question of certifying …

The abbreviations LMI and SOS stand for “linear matrix inequality" and “sum of squares,"
respectively. The cone n,2d of SOS polynomials in n variables of degree at most 2d is known …

The optimal allocation of resources for maximizing influence, spread of information or
coverage, has gained attention in the past years, in particular in machine learning and data …