Related papers: Mixed integer programming formulation of unsupervi…
We propose a supervised learning framework for computing solutions of multi-parametric Mixed Integer Linear Programs (MILPs) that arise in Model Predictive Control. Our approach also quantifies sub-optimality for the computed solutions.…
The deep extension of the restricted Boltzmann machine (RBM), known as the deep Boltzmann machine (DBM), is an expressive family of machine learning models which can serve as compact representations of complex probability distributions.…
Bringing together nonlinear optimization with polyhedral and integrality constraints enables versatile modeling, but poses significant computational challenges. We investigate a method to address these problems based on sequential…
Mixed Integer Linear Programs (MILPs) are highly flexible and powerful tools for modeling and solving complex real-world combinatorial optimization problems. Recently, machine learning (ML)-guided approaches have demonstrated significant…
A standard quadratic program is an optimization problem that consists of minimizing a (nonconvex) quadratic form over the unit simplex. We focus on reformulating a standard quadratic program as a mixed integer linear programming problem. We…
Mathematical programming is a branch of applied mathematics and has recently been used to derive new decoding approaches, challenging established but often heuristic algorithms based on iterative message passing. Concepts from mathematical…
We present exact mixed-integer linear programming formulations for verifying the performance of first-order methods for parametric quadratic optimization. We formulate the verification problem as a mixed-integer linear program where the…
For multiparametric mixed-integer convex programming problems such as those encountered in hybrid model predictive control, we propose an algorithm for generating a feasible partition of a subset of the parameter space. The result is a…
Mixed-integer optimization problems arise in a wide range of control applications. Benders decomposition is a widely used algorithm for solving such problems by decomposing them into a mixed-integer master problem and a continuous…
There has been a great deal of recent interest in binarized neural networks, especially because of their explainability. At the same time, automatic differentiation algorithms such as backpropagation fail for binarized neural networks,…
We present a mathematical construction for the restricted Boltzmann machine (RBM) that doesn't require specifying the number of hidden units. In fact, the hidden layer size is adaptive and can grow during training. This is obtained by first…
This paper proposes a novel primal heuristic for Mixed Integer Programs, by employing machine learning techniques. Mixed Integer Programming is a general technique for formulating combinatorial optimization problems. Inside a solver, primal…
Consider the setting of constrained optimization, with some parameters unknown at solving time and requiring prediction from relevant features. Predict+Optimize is a recent framework for end-to-end training supervised learning models for…
Mixed-integer linear programming (MILP) is widely employed for modeling combinatorial optimization problems. In practice, similar MILP instances with only coefficient variations are routinely solved, and machine learning (ML) algorithms are…
Mixed-integer optimisation problems can be computationally challenging. Here, we introduce and analyse two efficient algorithms with a specific sequential design that are aimed at dealing with sampled problems within this class. At each…
This paper introduces an improved recursive algorithm to generate the set of all nondominated objective vectors for the Multi-Objective Integer Programming (MOIP) problem. We significantly improve the earlier recursive algorithm of \"Ozlen…
We present strong mixed-integer programming (MIP) formulations for high-dimensional piecewise linear functions that correspond to trained neural networks. These formulations can be used for a number of important tasks, such as verifying…
This work proposes deep network models and learning algorithms for unsupervised and supervised binary hashing. Our novel network design constrains one hidden layer to directly output the binary codes. This addresses a challenging issue in…
Binary classification is one of the most common problem in machine learning. It consists in predicting whether a given element belongs to a particular class. In this paper, a new algorithm for binary classification is proposed using a…
Double machine learning is a statistical method for leveraging complex black-box models to construct approximately unbiased treatment effect estimates given observational data with high-dimensional covariates, under the assumption of a…