277 citations · 461 across the 25 of their papers we have counts for
9 papers · 1 filter
Efficient and robust high-dimensional sparse logistic regression via nonlinear primal-dual hybrid gradient algorithms
Jérôme Darbon, Gabriel P. Langlois
Logistic regression is a widely used statistical model to describe the relationship between a binary response variable and predictor variables in data sets. It is often used in mac…
Hopf-type representation formulas and efficient algorithms for certain high-dimensional optimal control problems
Paula Chen, Jérôme Darbon, Tingwei Meng
Two key challenges in optimal control include efficiently solving high-dimensional problems and handling optimal control problems with state-dependent running costs. In this paper,…
Lax-Oleinik-type formulas and efficient algorithms for certain high-dimensional optimal control problems
Paula Chen, Jérôme Darbon, Tingwei Meng
Two of the main challenges in optimal control are solving problems with state-dependent running costs and developing efficient numerical solvers that are computationally tractable…
Accelerated nonlinear primal-dual hybrid gradient methods with applications to supervised machine learning
Jérôme Darbon, Gabriel P. Langlois
The linear primal-dual hybrid gradient (PDHG) method is a first-order method that splits convex optimization problems with saddle-point structure into smaller subproblems. Unlike t…
On Hamilton-Jacobi PDEs and image denoising models with certain non-additive noise
Jérôme Darbon, Tingwei Meng, Elena Resmerita
We consider image denoising problems formulated as variational problems. It is known that Hamilton-Jacobi PDEs govern the solution of such optimization problems when the noise mode…
Neural network architectures using min-plus algebra for solving certain high dimensional optimal control problems and Hamilton-Jacobi PDEs
Jérôme Darbon, Peter M. Dower, Tingwei Meng
Solving high dimensional optimal control problems and corresponding Hamilton-Jacobi PDEs are important but challenging problems in control engineering. In this paper, we propose tw…
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…
A Caputo fractional derivative-based algorithm for optimization
Yeonjong Shin, Jérôme Darbon, George Em Karniadakis
We propose a novel Caputo fractional derivative-based optimization algorithm. Upon defining the Caputo fractional gradient with respect to the Cartesian coordinate, we present a ge…
Optimal Trajectories of a UAV Base Station Using Hamilton-Jacobi Equations
Marceau Coupechoux, Jérôme Darbon, Jean-Marc Kélif +1
We consider the problem of optimizing the trajectory of an Unmanned Aerial Vehicle (UAV). Assuming a traffic intensity map of users to be served, the UAV must travel from a given i…