article · ArXiv.org · 2025

$MC^2$ Mixed Integer and Linear Programming

Polson, Nick, Sokolov, Vadim

Cited by 0Open access

Abstract

In this paper, we design $MC^2$ algorithms for Mixed Integer and Linear Programming. By expressing a constrained optimisation as one of simulation from a Boltzmann distribution, we reformulate integer and linear programming as Monte Carlo optimisation problems. The key insight is that solving these optimisation problems requires the ability to simulate from truncated distributions, namely multivariate exponentials and Gaussians. Efficient simulation can be achieved using the algorithms of Kent and Davis. We demonstrate our methodology on portfolio optimisation and the classical farmer problem from stochastic programming. Finally, we conclude with directions for future research.

Cite this paper

APA 7

Polson, N., & Sokolov, V. (2025). $MC^2$ Mixed Integer and Linear Programming. ArXiv.org.

MLA 9

Polson, Nick, and Vadim Sokolov. “$MC^2$ Mixed Integer and Linear Programming.” ArXiv.org, 2025.

Chicago

Polson, Nick, and Vadim Sokolov. 2025. “$MC^2$ Mixed Integer and Linear Programming.” ArXiv.org.

Harvard

Polson, N. and Sokolov, V. (2025) ‘$MC^2$ Mixed Integer and Linear Programming’, ArXiv.org.

BibTeX

@article{polson2025mixed,
  title = {{$MC^2$ Mixed Integer and Linear Programming}},
  author = {Polson, Nick and Sokolov, Vadim},
  journal = {ArXiv.org},
  year = {2025}
}

Made from the index record. Check names, capitalisation and page numbers against the paper. Need another style? AI for Research has over 10,000.