mlsanityData to 14 Oct 2026

Optimization Problems for Machine Learning: A Survey

arXiv 1901.05331 ↗First posted 16 Jan 2019math.OC cs.LGcited by 15

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Abstract (arXiv)

This paper surveys the machine learning literature and presents in an optimization framework several commonly used machine learning approaches. Particularly, mathematical optimization models are presented for regression, classification, clustering, deep learning, and adversarial learning, as well as new emerging applications in machine teaching, empirical model learning, and Bayesian network structure learning. Such models can benefit from the advancement of numerical optimization techniques which have already played a distinctive role in several machine learning settings. The strengths and the shortcomings of these models are discussed and potential research directions and open problems are highlighted.

Key facts. Cited by 15 papers in the map (data through 14 Oct 2026). First posted on arXiv 16 Jan 2019.

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Citing papers per year: 2021: 6; 2022: 3; 2023: 4; 2024: 1; 2025: 1.

15 papers.

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  1. 2023When Deep Learning Meets Polyhedral Theory: A Surveycited by 39
  2. 2021Optimization with Constraint Learning: A Framework and Surveycited by 28
  3. 2021An Exact Algorithm for Semi-supervised Minimum Sum-of-Squares Clusteringcited by 13
  4. 2022An algorithm for clustering with confidence-based must-link and cannot-link constraintscited by 9
  5. 2022Margin Optimal Classification Treescited by 7
  6. 2021Community Detection in the Stochastic Block Model by Mixed Integer Programmingcited by 5
  7. 2021Rule Generation for Classification: Scalability, Interpretability, and Fairnesscited by 4
  8. 2023Global Optimization: A Machine Learning Approachcited by 4
  9. 2024Feed-Forward Neural Networks as a Mixed-Integer Programcited by 4
  10. 2021A reinforcement learning approach to resource allocation in genomic selectioncited by 3
  11. 2023AutoDOViz: Human-Centered Automation for Decision Optimizationcited by 3
  12. 2022Support Vector Machines with the Hard-Margin Loss: Optimal Training via Combinatorial Benders' Cutscited by 2
3 more
  1. 2021Machine Learning Models Disclosure from Trusted Research Environments (TRE), Challenges and Opportunitiescited by 1
  2. 2025Strong bounds for large-scale Minimum Sum-of-Squares Clusteringcited by 1
  3. 2023Optimizing accuracy and diversity: a multi-task approach to forecast combinationscited by 0