Related papers: Lipschitz Continuity of the Value Function in Mixe…
In this paper, we investigate optimal control problems subject to a semilinear elliptic partial differential equations. The cost functional contains a term that measures the size of the support of the control, which is the so-called…
The current study addresses the control problems posed by a semilinear neutral integro-differential equation with memory. The primary objectives of this study are to investigate the existence of a mild solution and approximate…
We consider a stochastic optimal control problem in a market model with temporary and permanent price impact, which is related to an expected utility maximization problem under finite fuel constraint. We establish the initial condition…
We deal with the approximate solution of initial value problems in infinite-dimensional Banach spaces with a Schauder basis. We only allow finite-dimensional algorithms acting in the spaces $\rr^N$, with varying $N$. The error of such…
We devise and analyze a reliable and efficient a posteriori error estimator for a semilinear control-constrained optimal control problem in two and three dimensional Lipschitz, but not necessarily convex, polytopal domains. We consider a…
This work focuses on indirect descent methods for optimal control problems governed by nonlinear ordinary differential equations in Banach spaces, viewed as abstract models of distributed dynamics. As a reference line, we revisit the…
The Markowitz problem consists of finding in a financial market a self-financing trading strategy whose final wealth has maximal mean and minimal variance. We study this in continuous time in a general semimartingale model and under cone…
The Lasso and the basis pursuit in compressed sensing and machine learning are convex optimization problems with three parameters: the regularization scalar, the observation vector and the data matrix. Relative to the first two parameters,…
We consider the stochastic Landau-Lifshitz-Bloch equation in dimensions 1,2,3, perturbed by a real-valued Wiener process. We consider a Suslin space-valued control process with a general control operator, which can depend on both the…
We examine the impact of learning Lipschitz continuous models in the context of model-based reinforcement learning. We provide a novel bound on multi-step prediction error of Lipschitz models where we quantify the error using the…
This work is a continuation of the previous one in [{\it Optimization} (2023)], where the existence of optimal solutions and first-order necessary optimality conditions in both Pontryagin's maximum principle form and the variational form…
Optimal control problems with oscillations (chattering controls) and concentrations (impulsive controls) can have integral performance criteria such that concentration of the control signal occurs at a discontinuity of the state signal.…
This paper proposes a relaxed control regularization with general exploration rewards to design robust feedback controls for multi-dimensional continuous-time stochastic exit time problems. We establish that the regularized control problem…
We would like to study the solution stability of a parametric control problem governed by semilinear elliptic equations with a mixed state-control constraint, where the cost function is nonconvex and the admissible set is unbounded. The…
We consider a class of infinite-dimensional singular stochastic control problems. These can be thought of as spatial monotone follower problems and find applications in spatial models of production and climate transition. Let…
We prove that solution operators of elliptic obstacle-type variational inequalities (or, more generally, locally Lipschitz continuous functions possessing certain pointwise-a.e. convexity properties) are Newton differentiable when…
We study differentiability properties of convex operators defined on a Banach space with values in an $\Lc_p$ space and of their compositions with monotonic convex functionals on this space. We develop new tools for operators enjoying an…
In this article, we investigate some of the fine properties of the value function associated to an optimal control problem in the Wasserstein space of probability measures. Building on new interpolation and linearisation formulas for…
In the present paper, a systematic study is made of quantitative semicontinuity (a.k.a. Lipschitzian) properties of certain multifunctions, which are defined as a solution map associated to a family of parameterized ``split" feasibility…
We prove the continuity of the value function of the sparse optimal control problem. The sparse optimal control is a control whose support is minimum among all admissible controls. Under the normality assumption, it is known that a sparse…