Mathematical Programming in Machine Learning and Artificial Intelligence: A Unified Taxonomy of Models and Applications
Abstract
Mathematical programming provides a common language for many decisions embedded in modern machine-learning (ML) and artificial-intelligence (AI) systems: selecting retrieval context, routing tokens, allocating inference compute, fitting structured predictors, protecting against distribution shift, and balancing competing objectives. However, the relevant literature is fragmented across optimization, information retrieval, recommendation, natural-language processing, computer vision, and learning theory. This paper organizes various applications under common mathematical programming paradigms: linear, quadratic, binary and mixed-integer, conic, bilevel, multi-objective, inverse, distributionally robust, submodular, and min--max optimization. We normalize the models with a mostly unified notation and, for every application, identify inputs, decision variables, a principal formulation, structural properties, solution strategies, and limitations. Across paradigms, we compare tractability, relaxation quality, decomposition, approximation guarantees, and scalability bottlenecks. The paper shows that mathematical programming is most useful not as a claim that all learning is LP or MIP, but as a disciplined interface between predictions and constrained decisions.
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BibTeX
@misc{dong2026mathematical,
title = {{Mathematical Programming in Machine Learning and Artificial Intelligence: A Unified Taxonomy of Models and Applications}},
author = {Chaosheng Dong},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.07254},
eprint = {2609.07254},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.07254},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Mathematical Programming in Machine Learning and Artificial Intelligence: A Unified Taxonomy of Models and Applications
AU - Chaosheng Dong
PY - 2026
DA - 2026/09/07
PB - arXiv
DO - 10.48550/arxiv.2609.07254
UR - https://arxiv.org/abs/2609.07254
AB - Mathematical programming provides a common language for many decisions embedded in modern machine-learning (ML) and artificial-intelligence (AI) systems: selecting retrieval context, routing tokens, allocating inference compute, fitting structured predictors, protecting against distribution shift, and balancing competing objectives. However, the relevant literature is fragmented across optimization, information retrieval, recommendation, natural-language processing, computer vision, and learning theory. This paper organizes various applications under common mathematical programming paradigms: linear, quadratic, binary and mixed-integer, conic, bilevel, multi-objective, inverse, distributionally robust, submodular, and min--max optimization. We normalize the models with a mostly unified notation and, for every application, identify inputs, decision variables, a principal formulation, structural properties, solution strategies, and limitations. Across paradigms, we compare tractability, relaxation quality, decomposition, approximation guarantees, and scalability bottlenecks. The paper shows that mathematical programming is most useful not as a claim that all learning is LP or MIP, but as a disciplined interface between predictions and constrained decisions.
ER -