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This paper establishes a statistical versus computational trade-off for solving a basic high-dimensional machine learning problem via a basic convex relaxation method. Specifically, we consider the {\em Sparse Principal Component Analysis}…

Satisfiability Modulo Theories (SMT) and SAT solvers are critical components in many formal software tools, primarily due to the fact that they are able to easily solve logical problem instances with millions of variables and clauses. This…

The Descriptor System Tools (DSTOOLS) is a collection of MATLAB functions for the operation on and manipulation of rational transfer function matrices via their descriptor system realizations. The DSTOOLS collection relies on the Control…

We study several questions related to diversifying search results. We give improved approximation algorithms in each of the following problems, together with some lower bounds. - We give a polynomial-time approximation scheme (PTAS) for a…

In a recent note [8], the author provides a counterexample to the global convergence of what his work refers to as "the DSOS and SDSOS hierarchies" for polynomial optimization problems (POPs) and purports that this refutes claims in our…

We consider extensions of the Shannon relative entropy, referred to as $f$-divergences.Three classical related computational problems are typically associated with these divergences: (a) estimation from moments, (b) computing normalizing…

This work focuses on effectively generating diverse solutions for satisfiability modulo theories (SMT) formulas, targeting the theories of bit-vectors, arrays, and uninterpreted functions, which is a critical task in software and hardware…

In this paper, we introduce a new class of nonsmooth convex functions called SOS-convex semialgebraic functions extending the recently proposed notion of SOS-convex polynomials. This class of nonsmooth convex functions covers many common…

In data-parallel computing frameworks, intermediate parallel data is often produced at various stages which needs to be transferred among servers in the datacenter network (e.g. the shuffle phase in MapReduce). A stage often cannot start or…

In this survey we consider polynomial optimization problems, asking to minimize a polynomial function over a compact semialgebraic set, defined by polynomial inequalities. This models a great variety of (in general, nonlinear nonconvex)…

The Subset-Sums Ratio problem (SSR) is an optimization problem in which, given a set of integers, the goal is to find two subsets such that the ratio of their sums is as close to 1 as possible. In this paper we develop a new FPTAS for the…

Structural operational semantics (SOS) is a technique for defining operational semantics for programming and specification languages. Because of its intuitive appeal and flexibility, SOS has found considerable application in the study of…

Type III methods were introduced by SAS to address difficulties in dummy-variable models for effects of multiple factors and covariates. They are widely used in practice; they are the default method in several statistical computing…

ESPResSo 4.0 is an extensible simulation package for research on soft matter. This versatile molecular dynamics program was originally developed for coarse-grained simulations of charged systems Limbach et al., Comput. Phys. Commun. 174,…

Modern software for propositional satisfiability problems gives a powerful automated reasoning toolkit, capable of outputting not only a satisfiable/unsatisfiable signal but also a justification of unsatisfiability in the form of resolution…

This chapter investigates how symmetries can be used to reduce the computational complexity in polynomial optimization problems. A focus will be specifically given on the Moment-SOS hierarchy in polynomial optimization, where results from…

Additive smooth models, such as Generalized additive models (GAMs) of location, scale, and shape (GAMLSS), are a popular choice for modeling experimental data. However, software available to fit such models is usually not tailored…

Simflowny is an open platform which automatically generates efficient parallel code of scientific dynamical models for different simulation frameworks. Here we present major upgrades on this software to support simultaneously a quite…

This paper studies generalized semi-infinite programs (GSIPs) given by polynomials. We propose a hierarchy of polynomial optimization relaxations to solve them. They are based on Lagrange multiplier expressions and polynomial extensions.…

Semidefinite relaxations are widely used to compute upper bounds on the objective of optimization problems involving noncommutative polynomials. Such optimization problems are prevalent in quantum information. We present an algorithm able…