Related papers: Optimal control of gradient flows via the Weighted…
We propose in this paper a gradient-type dynamical system to solve the problem of maximizing quantum observables for finite dimensional closed quantum ensembles governed by the controlled Liouville-von Neumann equation. The asymptotic…
We investigate a variational approach to nonpotential perturbations of gradient flows of nonconvex energies in Hilbert spaces. We prove existence of solutions to elliptic-in-time regularizations of gradient flows by combining the…
We consider a class of optimal control problems for measure-valued nonlinear transport equations describing traffic flow problems on networks. The objective isto minimise/maximise macroscopic quantities, such as traffic volume or average…
The paper is devoted to the study of a new class of optimal control problems for nonsmooth dynamical systems governed by nonconvex discontinuous differential inclusions of the sweeping type with involving variable time into optimization. We…
In this article, we discuss gradient robust discretizations for the simulation of non-linear incompressible Navier-Stokes problem and the optimal control of such flow. We consider several formulations of the flow problem that are equivalent…
We study a variant of the dynamical optimal transport problem in which the energy to be minimised is modulated by the covariance matrix of the distribution. Such transport metrics arise naturally in mean-field limits of certain ensemble…
We consider the well-known minimizing-movement approach to the definition of a solution of gradient-flow type equations by means of an implicit Euler scheme depending on an energy and a dissipation term. We perturb the energy by considering…
We investigate a well-known phenomenon of variational approaches in image processing, where typically the best image quality is achieved when the gradient flow process is stopped before converging to a stationary point. This paradox…
Bilevel optimization is a key framework in hierarchical decision-making, where one problem is embedded within the constraints of another. In this work, we propose a control-theoretic approach to solving bilevel optimization problems. Our…
We study the asymptotic behaviour of a gradient system in a regime in which the driving energy becomes singular. For this system gradient-system convergence concepts are ineffective. We characterize the limiting behaviour in a different…
We propose an adaptive optimization algorithm for solving unconstrained scaled gradient flow problems that achieves fast convergence by controlling the optimization trajectory shape and the discretization step sizes. Under a broad class of…
This paper studies the problem of optimal flow control in dynamic inventory systems. A dynamic optimal distribution problem, including time-varying supply and demand, capacity constraints on the transportation lines, and convex flow cost…
We consider the problem of dynamic optimal transport with a density constraint. We derive variational limits in terms of $\Gamma$-convergence for two singular phenomena. First, for densities constrained near a hyperplane we recover the…
This paper formalizes an optimal water-power flow (OWPF) problem to optimize the use of controllable assets across power and water systems while accounting for the couplings between the two infrastructures. Tanks and pumps are optimally…
We prove convergence of the proximal policy gradient method for a class of constrained stochastic control problems with control in both the drift and diffusion of the state process. The problem requires either the running or terminal cost…
We formulate and analyse an optimal control problem for the coagulation-fragmentation equation, where a scalar, time-dependent control modulates the coagulation rate by multiplying the coagulation kernel. The objective functional consists…
In this paper we present a variational technique that handles coarse-graining and passing to a limit in a unified manner. The technique is based on a duality structure, which is present in many gradient flows and other variational…
We address the problem of sampling from terminally constrained distributions with pre-trained flow-based generative models through an optimal control formulation. Theoretically, we characterize the value function by a…
The article discusses the gradient discretisation method (GDM) for distributed optimal control problems governed by diffusion equation with pure Neumann boundary condition. Using the GDM framework enables to develop an analysis that…
In this paper, we provide a mathematical framework for improving generalization in a class of learning problems which is related to point estimations for modeling of high-dimensional nonlinear functions. In particular, we consider a…