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math.OC2025
A fast algorithm for solving the lasso problem exactly without homotopy using differential inclusions
Gabriel P. Langlois, Jérôme Darbon
We prove in this work that the well-known lasso problem can be solved exactly without homotopy using novel differential inclusions techniques. Specifically, we show that a selectio…
math.OC2021
Connecting Hamilton--Jacobi partial differential equations with maximum a posteriori and posterior mean estimators for some non-convex priors
Jérôme Darbon, Gabriel P. Langlois, Tingwei Meng
Many imaging problems can be formulated as inverse problems expressed as finite-dimensional optimization problems. These optimization problems generally consist of minimizing the s…
math.OC2019
Overcoming the curse of dimensionality for some Hamilton--Jacobi partial differential equations via neural network architectures
Jerome Darbon, Gabriel P. Langlois, Tingwei Meng
We propose new and original mathematical connections between Hamilton-Jacobi (HJ) partial differential equations (PDEs) with initial data and neural network architectures. Specific…