Chordal and factor-width decomposition methods for semidefinite programming and
polynomial optimization have recently enabled the analysis and control of large-scale linear …

Outlier-robust estimation is a fundamental problem and has been extensively investigated
by statisticians and practitioners. The last few years have seen a convergence across …

We propose the first general and scalable framework to design certifiable algorithms for
robust geometric perception in the presence of outliers. Our first contribution is to show that …

Moment and polynomial optimization has received high attention in recent decades. It has
beautiful theory and efficient methods, as well as broad applications for various …

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 …

In recent years, semidefinite relaxations of common optimization problems in robotics have
attracted growing attention due to their ability to provide globally optimal solutions. In many …

A ubiquitous problem in quantum physics is to understand the ground-state properties of
many-body systems. Confronted with the fact that exact diagonalization quickly becomes …

This article focuses on optimization of polynomials in noncommuting variables, while taking
into account sparsity in the input data. A converging hierarchy of semidefinite relaxations for …

We provide a new hierarchy of semidefinite programming relaxations, called NCTSSOS, to
solve large-scale sparse noncommutative polynomial optimization problems. This hierarchy …

We consider solving high-order and tight semidefinite programming (SDP) relaxations of
nonconvex polynomial optimization problems (POPs) that often admit degenerate rank-one …