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We study a stochastic control problem for nonlinear systems governed by stochastic differential equations with irregular drift. The drift coefficient is assumed to decompose as $b(t,x,a)=b_1(t,x)+b_2(x)b_3(t,a)$, where $b_1$ is bounded and…

Optimization and Control · Mathematics 2026-04-02 Antoine Marie Bogso , Rhoss Likibi Pellat , Wilfried Kuissi Kamdem , Olivier Menoukeu Pamen

The paper presents an approach to studying optimal control problems in the space of nonnegative measures with dynamics given by a nonlocal balance law. This approach relies on transforming the balance law into a continuity equation in the…

Optimization and Control · Mathematics 2025-01-30 Nikolay Pogodaev , Maxim Staritsyn

We derive novel algorithms for optimization problems constrained by partial differential equations describing multiscale particle dynamics, including non-local integral terms representing interactions between particles. In particular, we…

Numerical Analysis · Mathematics 2021-09-09 Mildred Aduamoah , Benjamin D. Goddard , John W. Pearson , Jonna C. Roden

In this paper, we study a discrete-time stochastic optimal control problem under distribution uncertainty with convex control domain. By weak convergence method and Sion's minimax theorem, we obtain the variational inequality for cost…

Optimization and Control · Mathematics 2022-06-28 Mingshang Hu , Shaolin Ji , Xiaojuan Li

This paper proposes a fully data-driven approach for optimal control of nonlinear control-affine systems represented by a stochastic diffusion. The focus is on the scenario where both the nonlinear dynamics and stage cost functions are…

Optimization and Control · Mathematics 2025-11-03 Nicolas Hoischen , Petar Bevanda , Stefan Sosnowski , Sandra Hirche , Boris Houska

We present a neural network approach for approximating the value function of high-dimensional stochastic control problems. Our training process simultaneously updates our value function estimate and identifies the part of the state space…

Optimization and Control · Mathematics 2024-05-08 Xingjian Li , Deepanshu Verma , Lars Ruthotto

This paper considers the problem of partially observed optimal control for forward stochastic systems which are driven by Brownian motions and an independent Poisson random measure with a feature that the cost functional is of mean-field…

Probability · Mathematics 2014-03-19 Yaozhong Hu , David Nualart , Qing Zhou

In this paper, we study the maximum principle for stochastic optimal control problems of forward-backward stochastic difference systems (FBS{\Delta}Ss) where the uncertainty is modeled by a discrete time, finite state process, rather than…

Optimization and Control · Mathematics 2019-07-10 Shailin Ji , Haodong Liu

We consider the stochastic optimal control problem for the dynamical system of the stochastic differential equation driven by a local martingale with a spatial parameter. Assuming the convexity of the control domain, we obtain the…

Probability · Mathematics 2021-09-15 Jian Song , Meng Wang

This work presents a convex-optimization-based framework for analysis and control of nonlinear partial differential equations. The approach uses a particular weak embedding of the nonlinear PDE, resulting in a linear equation in the space…

Optimization and Control · Mathematics 2018-04-23 Milan Korda , Didier Henrion , Jean-Bernard Lasserre

In this work, we investigate a stochastic control framework for global optimization over both Euclidean spaces and the Wasserstein space of probability measures, where the objective function may be non-convex and/or non-differentiable. In…

Optimization and Control · Mathematics 2026-04-21 Jinniao Qiu

We obtain a maximum principle for stochastic control problem of general controlled stochastic differential systems driven by fractional Brownian motions (of Hurst parameter $H>1/2$). This maximum principle specifies a system of equations…

Optimization and Control · Mathematics 2012-03-15 Yuecai Han , Yaozhong Hu , Jian Song

A discretization of an optimal control problem of a stochastic parabolic equation driven by multiplicative noise is analyzed. The state equation is discretized by the continuous piecewise linear element method in space and by the backward…

Numerical Analysis · Mathematics 2021-02-23 Binjie Li

In this paper, we investigate an optimal control problem governed by parabolic equations with measure-valued controls over time. We establish the well-posedness of the optimal control problem and derive the first-order optimality condition…

Optimization and Control · Mathematics 2024-04-04 Wei Gong , Dongdong Liang

In this paper, optimal control problems governed by diffusion equations with Dirichlet and Neumann boundary conditions are investigated in the framework of the gradient discretisation method. Gradient schemes are defined for the optimality…

Numerical Analysis · Mathematics 2018-10-09 Jerome Droniou , Neela Nataraj , Devika Shylaja

Optimal control of interacting particles governed by stochastic evolution equations in Hilbert spaces is an open area of research. Such systems naturally arise in formulations where each particle is modeled by stochastic partial…

Probability · Mathematics 2025-11-27 Filippo de Feo , Fausto Gozzi , Andrzej Święch , Lukas Wessels

Stochastic maximum principle of nonlinear controlled forward-backward systems, where the set of strict (classical) controls need not be convex and the diffusion coefficient depends explicitly on the variable control, is an open problem…

Probability · Mathematics 2008-12-20 Seid Bahlali

This paper is concerned with the partial information optimal control problem of mean-field type under partial observation, where the system is given by a controlled mean-field forward-backward stochastic differential equation with…

Optimization and Control · Mathematics 2017-08-21 Qingxin Meng , Qiuhong Shi , Maoning Tang

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…

Optimization and Control · Mathematics 2025-05-27 Ashley Davey , Harry Zheng

In this work, we present numerical analysis for a distributed optimal control problem, with box constraint on the control, governed by a subdiffusion equation which involves a fractional derivative of order $\alpha\in(0,1)$ in time. The…

Numerical Analysis · Mathematics 2017-12-22 Bangti Jin , Buyang Li , Zhi Zhou