6 papers
A Proximal Primal-Dual Approach to Generalized JKO Schemes for Doubly Nonlinear Parabolic Equations
Luis M. Briceño-Arias, José A. Carrillo, Dante Kalise +2
Variational methods based on optimization strategies are proposed to numerically solve a large family of nonlinear partial differential equations. They are all particular instances…
Forward-backward algorithm for functions with locally Lipschitz gradient: applications to mean field games
Luis M. Briceno-Arias, Francisco José Silva, Xianjin Yang
In this paper, we provide a generalization of the forward-backward splitting algorithm for minimizing the sum of a proper convex lower semicontinuous function and a differentiable…
Approximation of deterministic mean field games under polynomial growth conditions on the data
Justina Gianatti, Francisco J. Silva, Ahmad Zorkot
We consider a deterministic mean field games problem in which a typical agent solves an optimal control problem where the dynamics is affine with respect to the control and the cos…
Proximity Operators of Perspective Functions with Nonlinear Scaling
Luis M. Briceño-Arias, Patrick L. Combettes, Francisco J. Silva
A perspective function is a construction which combines a base function defined on a given space with a nonlinear scaling function defined on another space and which yields a lower…
Approximation of deterministic mean field games with control-affine dynamics
Justina Gianatti, Francisco J. Silva
We consider deterministic mean field games where the dynamics of a typical agent is non-linear with respect to the state variable and affine with respect to the control variable. P…
Perspective Functions with Nonlinear Scaling
Luis M. Briceño-Arias, Patrick L. Combettes, Francisco J. Silva
The classical perspective of a function is a construction which transforms a convex function into one that is jointly convex with respect to an auxiliary scaling variable. Motivate…