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$MC^2$ Mixed Integer and Linear Programming

Published: November 25, 2025 | arXiv ID: 2511.20575v1

By: Nick Polson, Vadim Sokolov

Potential Business Impact:

Solves hard math problems using a new computer trick.

Business Areas:
A/B Testing Data and Analytics

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.

Country of Origin
🇺🇸 United States

Page Count
30 pages

Category
Statistics:
Computation