Motivated by its implications in the development of general purpose solvers for decomposable Mixed Integer Programs (MIP), we address a fundamental research question, that is to assess if good decomposition patterns can be consistently found by looking only at static properties of MIP input instances, or not. We adopt a data driven approach, devising a … Read more
We describe the fundamentals of algorithms for minimizing a smooth nonlinear function, and extensions of these methods to the sum of a smooth function and a convex nonsmooth function. Such objective functions are ubiquitous in data analysis applications, as we illustrate using several examples. We discuss methods that make use of gradient (first-order) information about … Read more
Distance Geometry is based on the inverse problem that asks to find the positions of points, in a Euclidean space of given dimension, that are compatible with a given set of distances. We briefly introduce the field, and discuss some open and promising research areas. ArticleDownload View PDF
Abstract—In this article, we introduce new techniques to solve the nonlinear regression problem and the nonlinear classification problem. Our benchmarks suggest that our method for regression is significantly more effective when compared to classical methods and our method for classification is competitive. Our list of classical methods includes least squares, random forests, decision trees, boosted … Read more
Recently, the 1-bit compressive sensing (1-bit CS) has been studied in the field of sparse signal recovery. Since the amplitude information of sparse signals in 1-bit CS is not available, it is often the support or the sign of a signal that can be exactly recovered with a decoding method. In this paper, we first … Read more
We analyze the convergence of stochastic gradient methods for bi-level optimization problems. We address two specific cases: first when the outer objective function can be expressed as a finite sum of independent terms, and next when both the outer and inner objective functions can be expressed as finite sums of independent terms. We assume Lipschitz … Read more
This paper presents an algorithm that solves optimization problems on a matrix manifold $\mathcal{M} \subseteq \mathbb{R}^{m \times n}$ with an additional rank inequality constraint. The algorithm resorts to well-known Riemannian optimization schemes on fixed-rank manifolds, combined with new mechanisms to increase or decrease the rank. The convergence of the algorithm is analyzed and a weighted … Read more
We present an online learning approach to variable branching in branch-and-bound for mixed-integer linear problems. Our approach consists in learning strong branching scores in an online fashion and in using them to take branching decisions. More specifically, numerical scores are used to rank the branching candidates. If, for a given variable, the learned approximation is … Read more
We present three new approximate versions of alternating direction method of multipliers (ADMM), all of which require only knowledge of subgradients of the subproblem objectives, rather than bounds on the distance to the exact subproblem solution. One version, which applies only to certain common special cases, is based on combining the operator-splitting analysis of the … Read more
We consider the decision problem of making causal conclusions from observational data. Typically, using standard matched pairs techniques, there is a source of uncertainty that is not usually quanti fied, namely the uncertainty due to the choice of the experimenter: two di fferent reasonable experimenters can easily have opposite results. In this work we present an alternative … Read more