In applications throughout science and engineering one is often faced with the challenge of
solving an ill-posed inverse problem, where the number of available measurements is …

In recent years, optimization theory has been greatly impacted by the advent of sum of
squares (SOS) optimization. The reliance of this technique on large-scale semidefinite …

Triangulations presents the first comprehensive treatment of the theory of secondary
polytopes and related topics. The text discusses the geometric structure behind the …

Modern massive datasets create a fundamental problem at the intersection of the
computational and statistical sciences: how to provide guarantees on the quality of statistical …

We solve a 20-year old problem posed by Yannakakis and prove that there exists no
polynomial-size linear program (LP) whose associated polytope projects to the traveling …

Semidefinite programs are convex optimisation problems involving a linear objective
function and a domain of positive semidefinite matrices. Over the last two decades, they …

In this paper, we address the basic geometric question of when a given convex set is the
image under a linear map of an affine slice of a given closed convex cone. Such a …

It is undeniable that geometric ideas have been very important to the foundations of modern
discrete optimization. The influence that geometric algorithms have in optimization was …

We solve a 20-year old problem posed by Yannakakis and prove that no polynomial-size
linear program (LP) exists whose associated polytope projects to the traveling salesman …

We expand the toolbox for studying Bell correlations in multipartite systems by introducing
permutationally invariant Bell inequalities (PIBIs) involving few-body correlators. First, we …