Related papers: Partition-based formulations for mixed-integer opt…

The ongoing decarbonisation of power systems is driving an increasing reliance on distributed energy resources, which introduces complex and nonlinear interactions that are difficult to capture in conventional optimisation models. As a…

In this work, we develop a novel input feature selection framework for ReLU-based deep neural networks (DNNs), which builds upon a mixed-integer optimization approach. While the method is generally applicable to various classification…

A convex partition of a point set P in the plane is a planar partition of the convex hull of P with empty convex polygons or internal faces whose extreme points belong to P. In a convex partition, the union of the internal faces give the…

Reverse engineering deep ReLU networks is a critical problem in understanding the complex behavior and interpretability of neural networks. In this research, we present a novel method for reconstructing deep ReLU networks by leveraging…

We develop fast algorithms and robust software for convex optimization of two-layer neural networks with ReLU activation functions. Our work leverages a convex reformulation of the standard weight-decay penalized training problem as a set…

Neural networks are increasingly used as surrogates in optimization problems to replace computationally expensive models. However, embedding ReLU neural networks in mathematical programs introduces significant computational challenges,…

When solving decision-making problems with mathematical optimization, some constraints or objectives may lack analytic expressions but can be approximated from data. When an approximation is made by neural networks, the underlying problem…

Set partitioning is a key component of many algorithms in machine learning, signal processing, and communications. In general, the problem of finding a partition that minimizes a given impurity (loss function) is NP-hard. As such, there…

Feed-forward ReLU neural networks partition their input domain into finitely many "affine regions" of constant neuron activation pattern and affine behaviour. We analyze their mathematical structure and provide algorithmic primitives for an…

This paper addresses the challenging issue of symmetry in mixed-integer convex optimization problems, which frequently arise in real-world applications such as the unit commitment problem. Although variable aggregation techniques have been…

Mixed-integer nonlinear optimization encompasses a broad class of problems that present both theoretical and computational challenges. We propose a new type of method to solve these problems based on a branch-and-bound algorithm with convex…

Techniques involving factorization are found in a wide range of applications and have enjoyed significant empirical success in many fields. However, common to a vast majority of these problems is the significant disadvantage that the…

Optimization problems involving minimization of a rank-one convex function over constraints modeling restrictions on the support of the decision variables emerge in various machine learning applications. These problems are often modeled…

In this paper we propose a variant of the linear least squares model allowing practitioners to partition the input features into groups of variables that they require to contribute similarly to the final result. The output allows…

This material provides thorough tutorials on some optimization techniques frequently used in various engineering disciplines, including convex optimization, linearization techniques and mixed-integer linear programming, robust optimization,…

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…

We reformulate the problem of modularity maximization over the set of partitions of a network as a conic optimization problem over the completely positive cone, converting it from a combinatorial optimization problem to a convex continuous…

We present a novel method for graph partitioning, based on reinforcement learning and graph convolutional neural networks. Our approach is to recursively partition coarser representations of a given graph. The neural network is implemented…

Recently, theoretical analyses of deep neural networks have broadly focused on two directions: 1) Providing insight into neural network training by SGD in the limit of infinite hidden-layer width and infinitesimally small learning rate…

We consider the mixed regression problem with two components, under adversarial and stochastic noise. We give a convex optimization formulation that provably recovers the true solution, and provide upper bounds on the recovery errors for…