In this paper we present novel data-driven optimization models for Support Vector Machines (SVM), with the aim of linearly separating two sets of points that have non-disjoint convex closures. Traditional classi cation algorithms assume that the training data points are always known exactly. However, real-life data are often subject to noise. To handle such uncertainty, we … Read more
In the present work, we consider Zuckerberg’s method for geometric convex-hull proofs introduced in [Geometric proofs for convex hull defining formulations, Operations Research Letters 44(5), 625–629 (2016)]. It has only been scarcely adopted in the literature so far, despite the great flexibility in designing algorithmic proofs for the completeness of polyhedral descriptions that it offers. … Read more
This paper studies the maximization of a polymatroid subject to a cardinality constraint. In particular, we consider the problem of improving the value of the greedy set by swapping one of its members with an element that does not belong to it. To achieve this goal, we first define a (set-based) post-greedy measure of curvature … Read more
Chance-constrained programming (CCP) is one of the most difficult classes of optimization problems that has attracted the attention of researchers since the 1950s. In this survey, we focus on cases when only a limited information on the distribution is available, such as a sample from the distribution, or the moments of the distribution. We first … Read more
Decision trees are among the most popular machine learning models and are used routinely in applications ranging from revenue management and medicine to bioinformatics. In this paper, we consider the problem of learning optimal binary classification trees with univariate splits. Literature on the topic has burgeoned in recent years, motivated both by the empirical suboptimality … Read more
We provide a tutorial-type review on stochastic dual dynamic programming (SDDP), as one of the state-of-the-art solution methods for large-scale multistage stochastic programs. Since introduced about 30 years ago for solving large-scale multistage stochastic linear programming problems in energy planning, SDDP has been applied to practical problems from several fields and is enriched by various … Read more
In this paper we propose an optimization framework for multi-markets portfolio management, where a central headquarter relies upon local affiliates for the market-wise selection of investment options. Being averse to risk, the headquarter endogenously selects the maximum expected loss (conditional value at risk) for the affiliates, who respond designing portfolios and selecting management fees. In … Read more
Efficient Global Optimization (EGO) is the canonical form of Bayesian optimization that has been successfully applied to solve global optimization of expensive-to-evaluate black-box problems. However, EGO struggles to scale with dimension, and offers limited theoretical guarantees. In this work, a trust-region framework for EGO (TREGO) is proposed and analyzed. TREGO alternates between regular EGO steps … Read more
In this paper, we address the Constrained Two-dimensional Guillotine Cutting Problem (C2GCP) and the Constrained Three-dimensional Guillotine Cutting Problem (C3GCP). These problems consist of cutting a rectangular two-/three-dimensional object with orthogonal guillotine cuts to produce ordered rectangular two-/three-dimensional items seeking the most valuable subset of items cut. They often appear in manufacturing settings that cut … Read more
In this paper, we address the Constrained Three-dimensional Guillotine Cutting Problem (C3GCP), which consists of cutting a larger cuboid block (object) to produce a limited number of smaller cuboid pieces (items) using orthogonal guillotine cuts only. This way, all cuts must be parallel to the object’s walls and generate two cuboid sub-blocks, and there is … Read more