Related papers: Reflected BSDEs and optimal control and stopping f…
In this paper, we study ergodic backward stochastic differential equations (EBSDEs for short), for which the underlying diffusion is assumed to be multiplicative and of at most linear growth. The fact that the forward process has an…
In this paper, we establish well-posedness of reflected McKean-Vlasov SDEs and their particle approximations in smooth non-convex domains. We prove convergence of the interacting particle system to the corresponding mean-field limit with…
This work addresses an optimal control problem constrained by a degenerate kinetic equation of parabolic-hyperbolic type. Using a hypocoercivity framework we establish the well-posedness of the problem and demonstrate that the optimal…
In this paper we introduce a new kind of Backward Stochastic Differential Equations, called ergodic BSDEs, which arise naturally in the study of optimal ergodic control. We study the existence, uniqueness and regularity of solution to…
In this paper we study by probabilistic techniques the convergence of the value function for a two-scale, infinite-dimensional, stochastic controlled system as the ratio between the two evolution speeds diverges. The value function is…
We examine the minimization of a quadratic cost functional composed of the output and the final state of abstract infinite-dimensional evolution equations in view of existence of solutions and optimality conditions. While the initial value…
We introduce a new and efficient numerical method for multicriterion optimal control and single criterion optimal control under integral constraints. The approach is based on extending the state space to include information on a "budget"…
Recently, it has become evident that submodularity naturally captures widely occurring concepts in machine learning, signal processing and computer vision. Consequently, there is need for efficient optimization procedures for submodular…
We prove well-posedness results for backward stochastic differential equations (BSDEs) and reflected BSDEs with an optional obstacle process in the case of appropriately weighted $\mathbb{L}^2$-data when the generator is integrated with…
We introduce the optimality question to the relaxation in multiple control problems described by Sobolev type nonlinear fractional differential equations with nonlocal control conditions in Banach spaces. Moreover, we consider the…
This manuscript addresses the analysis and design of feedback laws for the stabilization of bilinear control systems in infinite-dimensional spaces. It first examines weak, strong, and polynomial stabilization within a Hilbert space…
We study penalization coupled with time discretization for decoupled Markovian doubly reflected BSDEs with obstacles \(p_b(t,X_t)\le Y_t\le p_w(t,X_t)\). The DRBSDE is approximated by a penalized BSDE with parameter \(\lambda\) and…
This paper is concerned with the quasi-linear reflected backward stochastic partial differential equation (RBSPDE for short). Basing on the theory of backward stochastic partial differential equation and the parabolic capacity and…
We solve in mild sense Hamilton Jacobi Bellman equations, both in an infinite dimensional Hilbert space and in a Banach space, with lipschitz Hamiltonian and lipschitz continuous final condition, and asking only a weak regularizing property…
This paper is concerned with the distributed control and stabilization problems for linear discrete-time large scale systems with imposed constraints. The main contributions of this paper are: Firstly, by using the maximum principle…
An accelerated block coordinate descent (ABCD) method in Hilbert space is analyzed to solve the sparse optimal control problem via its dual. The finite element approximation of this method is investigated and convergence results are…
We study a finite horizon optimal control problem for the continuity equation under a weighted integral state constraint on the mass outside a fixed set. The model is cast in a Hilbert framework for densities. On a suitable invariant…
In this paper we present an extension to the case of $L^1$-controls of a famous result by Ball--Marsden--Slemrod on the obstruction to the controllability of bilinear control systems in infinite dimensional spaces.
We develop a computational framework for D-optimal experimental design for PDE-based Bayesian linear inverse problems with infinite-dimensional parameters. We follow a formulation of the experimental design problem that remains valid in the…
In this paper, a characterization of the solution of impulse control problems in terms of superharmonic functions is given. In a general Markovian framework, the value function of the impulse control problem is shown to be the minimal…