← Back to all news
arXiv AI By Chaosheng Dong

Mathematical Programming in Machine Learning and Artificial Intelligence: A Unified Taxonomy of Models and Applications

Read the original on arXiv AI →

The paper presents a unified taxonomy that classifies machine‑learning and artificial‑intelligence applications according to mathematical programming paradigms such as linear, quadratic, mixed‑integer, conic, bilevel, and others. It standardizes notation, identifies key inputs, decision variables, and principal formulations for each application, and discusses structural properties, solution strategies, and limitations. The authors compare tractability, relaxation quality, decomposition, approximation guarantees, and scalability across paradigms, emphasizing that mathematical programming serves as a disciplined interface between predictions and constrained decisions rather than a universal modeling claim.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv AI.

Related stories

arXiv AI
Aug 28

CG4AI: A Column Generation Framework for Training AI Models Under Constraints

CG4AI is a column generation framework that trains AI models while enforcing linear constraints on their outputs. It constructs a convex combination of models, using a master linear program to set mixture weights and a pricing subproblem to generate new models guided by dual variables, focusing on the most violated constraints. The method is applied to MNIST digit classification—demonstrating constraint learning, adversarial robustness, error correction, and output relabeling—and to multi‑commodity flow routing, achieving feasible predictors with higher accuracy than single‑model baselines.

By Youcef Magnouche, Abderrahmane Driouch, S\'ebastien Martin, Pierre Bauguion
agentsbenchmarkssafety
More like this →
arXiv Machine Learning
Oct 3

Reformulation-Contrastive Learning for Mixed Integer Programs

The paper introduces ReMILP, a reformulation‑contrastive learning framework that uses self‑supervision from equivalent formulations of mixed‑integer linear programs (MILPs). By distinguishing re‑descriptions and substitutions, the method trains a graph neural network and a hypernetwork to predict how variable embeddings transform under changes of variables, achieving invariance and equivariance without solver‑derived labels. The learned representations prove useful for tasks such as binary solution, constraint activity, and integrality gap prediction, and serve as a strong initialization for fine‑tuning.

By Ousema Bouaneni, Mathis Le Bail, Cl\'ement Elliker, Ma\"el Jenny, Sonia Vanier
ragfine-tuning
More like this →