Related papers: Infinite horizon value functions in the Wasserstei…
We develop a framework for generalized variational inference in infinite-dimensional function spaces and use it to construct a method termed Gaussian Wasserstein inference (GWI). GWI leverages the Wasserstein distance between Gaussian…
Solving Fredholm equations of the first kind is crucial in many areas of the applied sciences. In this work we adopt a probabilistic and variational point of view by considering a minimization problem in the space of probability measures…
In this article, we provide sufficient conditions under which the controlled vector fields solution of optimal control problems formulated on continuity equations are Lipschitz regular in space. Our approach involves a novel combination of…
The long-time average behavior of the value function in the calculus of variations is known to be connected to the existence of the limit of the corresponding Abel means. Still in the Tonelli case, such a limit is in turn related to the…
We consider a two-player zero-sum game with integral payoff and with incomplete information on one side, where the payoff is chosen among a continuous set of possible payoffs. We prove that the value function of this game is solution of an…
We show a connection between global unconstrained optimization of a continuous function $f$ and weak KAM theory for an eikonal-type equation arising also in ergodic control. A solution $v$ of the critical Hamilton-Jacobi equation is built…
In this article, a notion of viscosity solutions is introduced for first order path-dependent Hamilton-Jacobi-Bellman (PHJB) equations associated with optimal control problems for path-dependent evolution equations in Hilbert space. We…
A two-person zero-sum differential game with unbounded controls is considered. Under proper coercivity conditions, the upper and lower value functions are characterized as the unique viscosity solutions to the corresponding upper and lower…
We consider the problem of optimal multi-modes switching in finite horizon, when the state of the system, including the switching cost functions are arbitrary ($g_{ij}(t,x)\geq 0$). We show existence of the optimal strategy, and give when…
In finite-dimensions, minimal surfaces that fill in the space delineated by closed curves and have minimal area arose naturally in classical physics in several contexts. No such concept seems readily available in infinite dimensions. The…
In this manuscript we consider a class optimal control problem for stochastic differential delay equations. First, we rewrite the problem in a suitable infinite-dimensional Hilbert space. Then, using the dynamic programming approach, we…
We study the Hamilton-Jacobi equation for undiscounted exit time control problems with general nonnegative Lagrangians using the dynamic programming approach. We prove theorems characterizing the value function as the unique…
In this article, a notion of viscosity solutions is introduced for second order path-dependent Hamilton-Jacobi-Bellman (PHJB) equations associated with optimal control problems for path-dependent stochastic evolution equations in Hilbert…
We give a meaning to the Hamilton--Jacobi equation arising from mean-field spin glass models in the viscosity sense, and establish the corresponding well-posedness. Originally defined on the set of monotone probability measures, these…
Necessary optimality conditions in the form of the maximum principle for control problems with infinite time horizon are considered. Both finite and infinite values of objective functional are allowed since the concept of overtaking or…
In this article we study a finite horizon optimal control problem with monotone controls. We consider the associated Hamilton-Jacobi-Bellman (HJB) equation which characterizes the value function. We consider the totally discretized problem…
We revisit the linear programming approach to deterministic, continuous time, infinite horizon discounted optimal control problems. In the first part, we relax the original problem to an infinite-dimensional linear program over a measure…
We consider an infinite horizon portfolio problem with borrowing constraints, in which an agent receives labor income which adjusts to financial market shocks in a path dependent way. This path-dependency is the novelty of the model, and…
An optimal control problem related to the probability of transition between stable states for a thermally driven Ginzburg-Landau equation is considered. The value function for the optimal control problem with a spatial discretization is…
This paper is devoted to the study of fully nonlinear stochastic Hamilton-Jacobi (HJ) equations for the optimal stochastic control problem of ordinary differential equations with random coefficients. Under the standard Lipschitz continuity…