2 citations · 3 across the 16 of their papers we have counts for
21 papers
Asymptotic properties of non-coercive Hamiltonians with drift
Martino Bardi
We consider Hamiltonians associated to optimal control problems for affine systems on the torus. They are not coercive and are possibly unbounded from below in the direction of the…
Long-time behaviour of deterministic Mean Field Games with non-monotone interactions
Martino Bardi, Hicham Kouhkouh
We consider deterministic Mean Field Games (MFG) in all Euclidean space with a cost functional continuous with respect to the distribution of the agents and attaining its minima in…
Deep Relaxation of Controlled Stochastic Gradient Descent via Singular Perturbations
Martino Bardi, Hicham Kouhkouh
We consider a singularly perturbed system of stochastic differential equations proposed by Chaudhari et al. (Res. Math. Sci. 2018) to approximate the Entropic Gradient Descent in t…
Singular perturbations in stochastic optimal control with unbounded data
Martino Bardi, Hicham Kouhkouh
We study singular perturbations of a class of two-scale stochastic control systems with unbounded data. The assumptions are designed to cover some relaxation problems for deep neur…
An Eikonal equation with vanishing Lagrangian arising in Global Optimization
Martino Bardi, Hicham Kouhkouh
We show a connection between global unconstrained optimization of a continuous function and weak KAM theory for an eikonal-type equation arising also in ergodic control. A solu…
Liouville results for fully nonlinear equations modeled on Hörmander vector fields. I. The Heisenberg group
Martino Bardi, Alessandro Goffi
This paper studies Liouville properties for viscosity sub- and supersolutions of fully nonlinear degenerate elliptic PDEs, under the main assumption that the operator has a family…