Related papers: Optimality Conditions in Variational Form for Non-…
We consider a control problem where the state must reach asymptotically a target while paying an integral payoff with a non-negative Lagrangian. The dynamics is just continuous, and no assumptions are made on the zero level set of the…
An optimal control problem with a time-parameter is considered. The functional to be optimized includes the maximum over time-horizon reached by a function of the state variable, and so an $L^\infty$-term. In addition to the classical…
This paper treats a distributed optimal control problem for a tumor growth model of Cahn-Hilliard type including chemotaxis. The evolution of the tumor fraction is governed by a variational inequality corresponding to a double obstacle…
In this paper, we study representation formulas for finite-horizon optimal control problems with or without state constraints, unifying two different viewpoints: the Lagrangian and dynamic programming (DP) frameworks. In a recent work [1],…
Using the recent weighted generalized fractional order operators of Hattaf, a general fractional optimal control problem without constraints on the values of the control functions is formulated and a corresponding (weak) version of…
We consider a class of stochastic control problems which has been widely used in optimal foraging theory. The state processes have two distinct dynamics, characterized by two pairs of drift and diffusion coefficients, depending on whether…
We study a control problem where the state equation is a nonlinear partial differential equation of the calculus of variation in a bounded domain, perturbed by noise. We allow the control to act on the boundary and set stochastic boundary…
The optimal control problem of stochastic systems is commonly solved via robust or scenario-based optimization methods, which are both challenging to scale to long optimization horizons. We cast the optimal control problem of a stochastic…
In this paper we develop necessary conditions for optimality, in the form of the stochastic Pontryagin maximum principle, for controlled equations with pointwise delay in the state and with control dependent noise, in the general case of…
We discuss first order optimality conditions for geometric optimization problems with Neumann boundary conditions and boundary observation. The methods we develop here are applicable to large classes of state systems or cost functionals.…
In this paper the necessary conditions of optimality in the form of maximum principle are derived for a very general class of variational problems. This class includes problems with any optimization criteria and constraints that can be…
We consider stochastic optimization problems involving an expected value of a nonlinear function of a base random vector and a conditional expectation of another function depending on the base random vector, a dependent random vector, and…
In this article, we derive first-order necessary optimality conditions for a constrained optimal control problem formulated in the Wasserstein space of probability measures. To this end, we introduce a new notion of localised metric…
In this paper we present a dynamic programing approach to stochastic optimal control problems with dynamic, time-consistent risk constraints. Constrained stochastic optimal control problems, which naturally arise when one has to consider…
We investigate optimal control problems with $L^0$ constraints, which restrict the measure of the support of the controls. We prove necessary optimality conditions of Pontryagin maximum principle type. Here, a special control perturbation…
Optimization problems with convex quadratic cost and polyhedral constraints are ubiquitous in signal processing, automatic control and decision-making. We consider here an enlarged problem class that allows to encode logical conditions and…
We study the reduction by symmetry for optimality conditions in optimal control problems of left-invariant affine multi-agent control systems, with partial symmetry breaking cost functions for continuous-time and discrete-time systems. We…
This paper deals with partially-observed optimal control problems for the state governed by stochastic differential equation with delay. We develop a stochastic maximum principle for this kind of optimal control problems using a variational…
This technical note considers a distributed convex optimization problem with nonsmooth cost functions and coupled nonlinear inequality constraints. To solve the problem, we first propose a modified Lagrangian function containing local…
In this paper we consider optimal control problems where the control variable is a potential and the state equation is an elliptic partial differential equation of a Schr\"odinger type, governed by the Laplace operator. The cost functional…