# Laplace Meets Moreau: Smooth Approximation to Infimal Convolutions Using Laplace's Method

arXiv: https://arxiv.org/abs/2406.02003 · HTML: https://mlsanity.com/paper/2406.02003/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jun 2024.

## Built on by (most cited first, 7 of 7)

- [Accuracy Improvements for Convolutional and Differential Distance Function Approximations](https://mlsanity.com/paper/2412.09200/) (2024)
- [Preconditioned Regularized Wasserstein Proximal Sampling](https://mlsanity.com/paper/2509.01685/) (2025)
- [Thinking Out of the Box: Hybrid SAT Solving by Unconstrained Continuous Optimization](https://mlsanity.com/paper/2506.00674/) (2025)
- [Accelerated Regularized Wasserstein Proximal Sampling Algorithms](https://mlsanity.com/paper/2601.09848/) (2026)
- [Probabilistic Gaussian Homotopy: A Probability-Space Continuation Framework for Nonconvex Optimization](https://mlsanity.com/paper/2603.13546/) (2026)
- [Implicit Neural Optimal Transport via Fixed-Point Optimization](https://mlsanity.com/paper/2605.10792/) (2026)
- [Points as Tori: Fast Pointwise Signed Distance for Point Clouds](https://mlsanity.com/paper/2607.16946/) (2026)

## Abstract (arXiv)

We study approximations to the Moreau envelope -- and infimal convolutions more broadly -- based on Laplace's method, a classical tool in analysis which ties certain integrals to suprema of their integrands. We believe the connection between Laplace's method and infimal convolutions is generally deserving of more attention in the study of optimization and partial differential equations, since it bears numerous potentially important applications, from proximal-type algorithms to solving Halmiton-Jacobi equations.