Related papers: Infinite horizon value functions in the Wasserstei…
In this paper, we show that the value functions of mean field control problems with common noise are the unique viscosity solutions to fully second-order Hamilton-Jacobi-Bellman equations, in a Crandall-Lions-like framework. We allow the…
We investigate the large-time behavior of the value functions of the optimal control problems on the $n$-dimensional torus which appear in the dynamic programming for the system whose states are governed by random changes. From the point of…
This paper is devoted to the analysis of a finite horizon discrete-time stochastic optimal control problem, in presence of constraints. We study the regularity of the value function which comes from the dynamic programming algorithm. We…
An optimal control problem in the space of probability measures, and the viscosity solutions of the corresponding dynamic programming equations defined using the intrinsic linear derivative are studied. The value function is shown to be…
An abstract framework guaranteeing the local continuous differentiability of the value function associated with optimal stabilization problems subject to abstract semilinear parabolic equations subject to a norm constraint on the controls…
In this work, we consider the local Cahn-Hilliard-Navier-Stokes equation with regular potential in two dimensional bounded domain. We formulate distributed optimal control problem as the minimization of a suitable cost functional subject to…
Path Integral Control methods were developed for stochastic optimal control covering a wide class of finite horizon formulations with control affine nonlinear dynamics. Characteristic for this class is that the HJB equation is linear and…
We study the Bellman equation in the Wasserstein space arising in the study of mean field control problems, namely stochastic optimal control problems for McKean-Vlasov diffusion processes.Using the standard notion of viscosity solution \`a…
We establish new results for path-dependent Hamilton-Jacobi equations with nonlinear monotone, and coercive operators on Hilbert space, which were initially studied in Bayraktar and Keller [J. Funct. Anal., 275 (8) (2018), pp. 2096-2161].…
We establish the well-posedness of viscosity solutions for a class of semi-linear Hamilton-Jacobi equations set on the space of probability measures on the torus. In particular, we focus on equations with both common and idiosyncratic…
This paper develops a comparison theorem for viscosity solutions of a new class of Hamilton-Jacobi-Bellman (HJB) equations, which is used to solve the separated problem governed by the K-S equation in the Wasserstein space. A distinctive…
We formulate a path-dependent stochastic optimal control problem under general conditions, for which weprove rigorously the dynamic programming principle and that the value function is the unique Crandall-Lions viscosity solution of the…
An abstract framework guaranteeing the continuous differentiability of local value functions on $H^1(\Omega)$ associated with optimal stabilization problems subject to abstract semilinear parabolic equations in the presence of norm…
We consider the problem of impulse control minimax in finite horizon, when cost functions $(C(t,x,\xi)>0)$. We show existence of value function of the problem. Moreover, the value function is characterized as the unique viscosity solution…
In this work we prove an analogue, for partial differential equations on the space of probability measures, of the classical vanishing viscosity result known for equations on the Euclidean space. Our result allows in particular to show that…
This paper continues the study of controlled interacting particle systems with common noise started in [W. Gangbo, S. Mayorga and A. \'{S}wi\k{e}ch, SIAM J. Math. Anal. 53 (2021), no. 2, 1320--1356] and [S. Mayorga and A. \'{S}wi\k{e}ch,…
This paper presents a finite-dimensional approximation for a class of partial differential equations on the space of probability measures. These equations are satisfied in the sense of viscosity solutions. The main result states the…
We establish a comparison principle for viscosity solutions of a class of nonlinear partial differential equations posed on the space of nonnegative finite measures, thereby extending recent results for PDEs defined on the Wasserstein space…
In this paper we investigate solutions to a linear Hamilton-Jacobi equations in the Wasserstein space of probability vectors on a finite simply connected graph. We prove that there exists a solution under the assumption that the initial…
This paper discusses a class of combinatorial optimization problems with uncertain costs in the objective function. It is assumed that a sample of the cost realizations is available, which defines an empirical probability distribution for…