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We consider a microgrid where different prosumers exchange energy altogether by the edges of a given network. Each prosumer is located to a node of the network and encompasses energy consumption, energy production and storage capacities…

Optimization and Control · Mathematics 2019-12-24 Pierre Carpentier , Jean-Philippe Chancelier , Michel de Lara , François Pacaud

This paper considers the learning of Boolean rules in either disjunctive normal form (DNF, OR-of-ANDs, equivalent to decision rule sets) or conjunctive normal form (CNF, AND-of-ORs) as an interpretable model for classification. An integer…

Artificial Intelligence · Computer Science 2020-08-07 Sanjeeb Dash , Oktay Günlük , Dennis Wei

Constructing complex computation from simpler building blocks is a defining problem of computer science. In algebraic automata theory, we represent computing devices as semigroups. Accordingly, we use mathematical tools like products and…

Group Theory · Mathematics 2025-05-06 Attila Egri-Nagy , Chrystopher L. Nehaniv

Differentiable optimization has received a significant amount of attention due to its foundational role in the domain of machine learning based on neural networks. This paper proposes a differentiable layer, named Differentiable Frank-Wolfe…

Machine Learning · Computer Science 2024-04-01 Zixuan Liu , Liu Liu , Xueqian Wang , Peilin Zhao

We tackle the problem of accelerating column generation (CG) approaches to set cover formulations in operations research. At each iteration of CG we generate a dual solution that approximately solves the LP over all columns consisting of a…

Data Structures and Algorithms · Computer Science 2021-03-30 Naveen Haghani , Julian Yarkony , Amelia Regan

We first propose a concise singular value decomposition of dual matrices. Then, the randomized version of the decomposition is presented. It can significantly reduce the computational cost while maintaining the similar accuracy. We analyze…

Numerical Analysis · Mathematics 2024-07-25 Mengyu Wang , Jingchun Zhou , Hanyu Li

In many manufacturing processes, batch processing is frequently needed for capacity reasons. This applies both to parallel and serial batching. However, while the serial batch processing is largely studied in the literature, as it is…

Optimization and Control · Mathematics 2024-02-14 Arianna Alfieri , Alessandro Druetto , Andrea Grosso , Fabio Salassa

We develop a system-theoretic framework for the structured analysis of distributed optimization algorithms with decomposable cost functions. We model such algorithms as a network of interacting dynamical systems and derive tests for…

Optimization and Control · Mathematics 2026-04-14 Aron Karakai , Jaap Eising , Andrea Martinelli , Florian Dörfler

Nonnegative matrix factorization arises widely in machine learning and data analysis. In this paper, for a given factorization of rank r, we consider the sparse stochastic matrix factorization (SSMF) of decomposing a prescribed m-by-n…

Numerical Analysis · Mathematics 2022-07-19 Guiyun Xiao , Zheng-Jian Bai , Wai-Ki Ching

Deep learning is a powerful tool for solving nonlinear differential equations, but usually, only the solution corresponding to the flattest local minimizer can be found due to the implicit regularization of stochastic gradient descent. This…

Numerical Analysis · Mathematics 2021-03-17 Yiqi Gu , Chunmei Wang , Haizhao Yang

The numerical performance of algorithms can be studied using test sets or procedures that generate such problems. This paper proposes various methods for generating linear, semidefinite, and second-order cone optimization problems.…

Optimization and Control · Mathematics 2023-02-03 Mohammadhossein Mohammadisiahroudi , Ramin Fakhimi , Brandon Augustino , Tamás Terlaky

The purpose of this survey is to serve both as a gentle introduction and a coherent overview of state-of-the-art Frank--Wolfe algorithms, also called conditional gradient algorithms, for function minimization. These algorithms are…

We present a distributed anytime algorithm for performing MAP inference in graphical models. The problem is formulated as a linear programming relaxation over the edges of a graph. The resulting program has a constraint structure that…

Artificial Intelligence · Computer Science 2012-02-20 Joop van de Ven , Fabio Ramos

Solving symmetric positive definite linear problems is a fundamental computational task in machine learning. The exact solution, famously, is cubicly expensive in the size of the matrix. To alleviate this problem, several linear-time…

Machine Learning · Computer Science 2017-06-02 Filip de Roos , Philipp Hennig

Model explainability is crucial for human users to be able to interpret how a proposed classifier assigns labels to data based on its feature values. We study generalized linear models constructed using sets of feature value rules, which…

Machine Learning · Statistics 2023-11-06 Sanjeeb Dash , Soumyadip Ghosh , Joao Goncalves , Mark S. Squillante

A class of finite-state and discrete-time optimal control problems is introduced. The problems involve a large number of agents with independent dynamics, which interact through an aggregative term in the cost function. The problems are…

Optimization and Control · Mathematics 2023-07-10 Kang Liu , Nadia Oudjane , Laurent Pfeiffer

In this paper, we consider the problem of generating a set of counterfactual explanations for a group of instances, with the one-for-many allocation rule, where one explanation is allocated to a subgroup of the instances. For the first…

Machine Learning · Computer Science 2024-02-16 Andrea Lodi , Jasone Ramírez-Ayerbe

We present a matrix-factorization algorithm that scales to input matrices with both huge number of rows and columns. Learned factors may be sparse or dense and/or non-negative, which makes our algorithm suitable for dictionary learning,…

Machine Learning · Statistics 2017-11-15 Arthur Mensch , Julien Mairal , Bertrand Thirion , Gael Varoquaux

We present a branch-cut-and-price framework to solve Cutting Stock Problems with strong relaxations using Set Covering (Packing) Formulations, which are solved by column generation. The main contributions of this paper include an extended…

Optimization and Control · Mathematics 2025-05-15 Renan F. F. da Silva , Rafael C. S. Schouery

Neural network compression empowers the effective yet unwieldy deep convolutional neural networks (CNN) to be deployed in resource-constrained scenarios. Most state-of-the-art approaches prune the model in filter-level according to the…

Computer Vision and Pattern Recognition · Computer Science 2019-06-26 Wenxiao Wang , Cong Fu , Jishun Guo , Deng Cai , Xiaofei He