相关论文: Viscosity Solutions for McKean-Vlasov Control on a…
We study optimization problems whereby the optimization variable is a probability measure. Since the probability space is not a vector space, many classical and powerful methods for optimization (e.g., gradients) are of little help. Thus,…
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…
In this paper, we study a stochastic recursive optimal control problem in which the objective functional is described by the solution of a backward stochastic differential equation driven by G-Brownian motion. Under standard assumptions, we…
It has been pointed out in the work [F. Gozzi et.al., \emph{Arch. Ration. Mech. Anal.} {163}(4) (2002), 295--327] that the existence and uniqueness of viscosity solutions to the first-order Hamilton-Jacobi-Bellman equation (HJBE) associated…
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…
In this paper, we prove a comparison result between semicontinuous viscosity sub and supersolutions growing at most quadratically of second-order degenerate parabolic Hamilton-Jacobi-Bellman and Isaacs equations. As an application, we…
The purpose of this paper is to review and highlight some connections between the problem of nonlinear smoothing and optimal control of the Liouville equation. The latter has been an active area of recent research interest owing to work in…
In the Dynamic Programming approach to optimal control problems a crucial role is played by the value function that is characterized as the unique viscosity solution of a Hamilton-Jacobi-Bellman (HJB) equation. It is well known that this…
The main result of this paper is to prove that viscosity solutions to a parabolic free boundary problem with variable coefficients are Lipschitz continuous under the assumptions that the solution has a Lipschitz free boundary and satisfies…
In this paper, we consider the mean field optimal switching problem with a Markov chain under viscosity solution notion. Based on the conditional distribution of the Markov chain, the value function and corresponding dynamic programming…
This paper deals with a stochastic recursive optimal control problem, where the diffusion coefficient depends on the control variable and the control domain is not necessarily convex. We focus on the connection between the general maximum…
We consider the minimization over probability measures of the expected value of a random variable, regularized by relative entropy with respect to a given probability distribution. In the general setting we provide a complete…
This paper provides a variational analysis of the unconstrained formulation of the LASSO problem, ubiquitous in statistical learning, signal processing, and inverse problems. In particular, we establish smoothness results for the optimal…
In this manuscript, we study optimal control problems for stochastic delay differential equations using the dynamic programming approach in Hilbert spaces via viscosity solutions of the associated Hamilton-Jacobi-Bellman equations. We show…
We deal with the convergence of the value function of an approximate control problem with uncertain dynamics to the value function of a nonlinear optimal control problem. The assumptions on the dynamics and the costs are rather general and…
We analyze stability of conservative solutions of the Cauchy problem on the line for the (integrated) Hunter-Saxton (HS) equation. Generically, the solutions of the HS equation develop singularities with steep gradients while preserving…
The purpose of this work is to provide a finite dimensional approximation of the solution to a mean field optimal control problem set on the $d$-dimensional torus. The approximation is obtained by means of a Fourier-Galerkin method, the…
We study a stochastic control problem for a Volterra-type controlled forward equation with past dependence obtained via convolution with a deterministic kernel. To be able to apply dynamic programming to solve the problem, we lift it to…
In this article, we propose a general framework for the study of differential inclusions in the Wasserstein space of probability measures. Based on earlier geometric insights on the structure of continuity equations, we define solutions of…
This paper analyzes a class of impulse control problems for multi-dimensional jump diffusions in the finite time horizon. Following the basic mathematical setup from Stroock and Varadhan \cite{StroockVaradhan06}, this paper first…