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We consider an optimal control problem subject to a semilinear elliptic PDE together with its variational discretization. We provide a condition which allows to decide whether a solution of the necessary first order conditions is a global…
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…
In the framework of a real Hilbert space we consider the problem of approaching solutions to a class of hierarchical variational inequality problems, subsuming several other problem classes including certain mathematical programs under…
We study linear-quadratic optimal control problems for Voterra systems, and problems that are linear-quadratic in the control but generally nonlinear in the state. In the case of linear-quadratic Volterra control, we obtain sharp necessary…
We study risk-sensitive control of continuous time Markov chains taking values in discrete state space. We study both finite and infinite horizon problems. In the finite horizon problem we characterise the value function via HJB equation…
This paper is concerned with second-order optimality conditions for Tikhonov regularized optimal control problems governed by the obstacle problem. Using a simple observation that allows to characterize the structure of optimal controls on…
An iterative learning algorithm is presented for continuous-time linear-quadratic optimal control problems where the system is externally symmetric with unknown dynamics. Both finite-horizon and infinite-horizon problems are considered. It…
We show that necessary and sufficient conditions of optimality in periodic optimization problems can be stated in terms of a solution of the corresponding HJB inequality, the latter being equivalent to a max-min type variational problem…
This paper investigates the near optimal control for a kind of linear stochastic control systems governed by the forward backward stochastic differential equations, where both the drift and diffusion terms are allowed to depend on controls…
This paper studies an infinite horizon optimal control problem for discrete-time linear system and quadratic criteria, both with random parameters which are independent and identically distributed with respect to time. In this general…
This paper gives an existence result for solutions to an elliptic optimal control problem based on a general fractional kernel, where the admissible controls come from a class satisfying both a growth bound and a superlinear-subcritical…
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…
We study a family of optimal control problems in which one aims at minimizing a cost that mixes a quadratic control penalization and the variance of the system, both for finitely many agents and for the mean-field dynamics as their number…
We consider an optimal control problem in which the state is governed by an unilateral obstacle problem (with obstacle from below) and restricted by a pointwise state constraint (from above). In the presence of control constraints, we…
We consider the variational discretization of a linear-quadratic optimal control problem with pointwise control and state constraints. In order to allow for a Fr\'echet smooth norm, the problem is reformulated by means of a reflexive…
We consider linear model reduction in both the control and state variables for unconstrained linear-quadratic optimal control problems subject to time-varying parabolic PDEs. The first-order optimality condition for a state-space reduced…
This paper is concerned with a stochastic linear quadratic (LQ, for short) control problem with a recursive cost functional in an infinite horizon. A main difficult is well-posedness of the BSDE in $L^1$ and in infinite horizon. A notion of…
The paper concerns the study of equilibrium points, namely the stationary solutions to the closed loop equation, of an infinite dimensional and infinite horizon boundary control problem for linear partial differential equations. Sufficient…
An optimal control problem with an infinite horizon quadratic cost functional for a linear system with a known additive disturbance is considered. The feature of this problem is that a weight matrix of the control cost in the cost…
We study an optimal control problem on infinite time horizon with semimartingale strategies, random coefficients and regime switching. The value function and the optimal strategy can be characterized in terms of three systems of backward…