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 …

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 …

We survey two aspects of mixed-integer nonlinear programming which have attracted less
attention (so far) than solution methods, solvers and applications: namely, whether the class …

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 …

We consider the problem of whether a given decision model, working with structured data,
has individual fairness. Following the work of Dwork, a model is individually biased (or …

Comparing probability distributions is an indispensable and ubiquitous task in machine
learning and statistics. The most common way to compare a pair of Borel probability …

Big data provide new opportunities to tackle one of the main difficulties in decision-making
systems—the uncertain behavior that follows unknown probability distribution. Standard …

Many real-world optimization problems involve uncertain parameters with probability
distributions that can be estimated using contextual feature information. In contrast to the …

The ROLMIP (Robust LMI Parser) is a toolbox specialized in control theory for uncertain
linear systems, built to work under MATLAB jointly with YALMIP, to ease the programming of …

The Sum-of-Squares (SoS) hierarchy is a semi-definite programming meta-algorithm that
captures state-of-the-art polynomial time guarantees for many optimization problems such …