A wide range of problems can be modeled as Mixed Integer Linear Programming (MIP)
problems using standard formulation techniques. However, in some cases the resulting MIP …

Nonnegative matrix factorization (NMF) has become a widely used tool for the analysis of
high-dimensional data as it automatically extracts sparse and meaningful features from a set …

Identifying the underlying structure of a data set and extracting meaningful information is a
key problem in data analysis. Simple and powerful methods to achieve this goal are linear …

A popular method in combinatorial optimization is to express polytopes P, which may
potentially have exponentially many facets, as solutions of linear programs that use few …

We introduce a method for proving lower bounds on the efficacy of semidefinite
programming (SDP) relaxations for combinatorial problems. In particular, we show that the …

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 …

We prove super-polynomial lower bounds on the size of linear programming relaxations for
approximation versions of constraint satisfaction problems. We show that for these problems …

Stochastic convex optimization, by which the objective is the expectation of a random
convex function, is an important and widely used method with numerous applications in …

Abstract Let M ∈ R^ p * q M∈ R p× q be a nonnegative matrix. The positive semidefinite
rank (psd rank) of M is the smallest integer k for which there exist positive semidefinite …

An extended formulation of a polytope P is a system of linear inequalities and equations that
describe some polyhedron which can be projected onto P. Extended formulations of small …