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We consider a stochastic control problem, where the control domain is convex and the system is governed by a nonlinear backward stochastic differential equation. With a L1 terminal data, we derive necessary optimality conditions in the form…

Probability · Mathematics 2008-07-23 Seid Bahlali

Recent work linking deep neural networks and dynamical systems opened up new avenues to analyze deep learning. In particular, it is observed that new insights can be obtained by recasting deep learning as an optimal control problem on…

Optimization and Control · Mathematics 2020-07-21 Weinan E , Jiequn Han , Qianxiao Li

We study the convergence problem of mean-field control theory in the presence of state constraints and non-degenerate idiosyncratic noise. Our main result is the convergence of the value functions associated to stochastic control problems…

Optimization and Control · Mathematics 2023-06-02 Samuel Daudin

In this paper we study a Pontryagin type stochastic maximum principle for the optimal control of a system, where the state dynamics satisfy a stochastic partial differential equation (SPDE) driven by a two-parameter (time-space) Brownian…

Optimization and Control · Mathematics 2024-01-03 Nacira Agram , Bernt Øksendal , Frank Proske , Olena Tymoshenko

We consider a class of optimal control problems, with finite or infinite horizon, for a continuous-time Markov chain with finite state space. In this case, the control process affects the transition rates. We suppose that the controlled…

Optimization and Control · Mathematics 2026-02-19 Fulvia Confortola , Marco Fuhrman

This paper is concerned with the maximum principle of stochastic optimal control problems, where the coefficients of the state equation and the cost functional are uncertain, and the system is generally under Markovian regime switching.…

Optimization and Control · Mathematics 2025-04-15 Tao Hao , Jiaqiang Wen , Jie Xiong

This article is concerned with an optimal control problem derived by mean-field forward-backward stochastic differential equation with noisy observation, where the drift coefficients of the state equation and the observation equation are…

Optimization and Control · Mathematics 2017-01-09 Guangchen Wang , Hua Xiao , Guojing Xing

We investigate a stochastic optimal control problem where the controlled system is depicted as a stochastic differential delayed equation; however, at the terminal time, the state is constrained in a convex set. We firstly introduce an…

Probability · Mathematics 2017-05-12 Jiaqiang Wen , Yufeng Shi

We show that mean field optimal controls satisfy a first order optimality condition (at a.e. time) without any a priori requirement on their spatial regularity. This principle is obtained by a careful limit procedure of the Pontryagin…

Analysis of PDEs · Mathematics 2025-04-02 Stefano Almi , Riccardo Durastanti , Francesco Solombrino

The purpose of this paper is to provide a detailed probabilistic analysis of the optimal control of nonlinear stochastic dynamical systems of the McKean Vlasov type. Motivated by the recent interest in mean field games, we highlight the…

Probability · Mathematics 2013-03-26 René Carmona , Francois Delarue

A stochastic procedure is developed which allows one to express Pontryagin's maximum principle for dissipative quantum system solely in terms of stochastic wave functions. Time-optimal controls can be efficiently computed without computing…

Quantum Physics · Physics 2020-11-09 Chungwei Lin , Dries Sels , Yanting Ma , Yebin Wang

This note outlines a mean-field approach to dynamic optimal transport problems based on the recently proposed McKean-Pontryagin maximum principle. Key aspects of the proposed methodology include i) avoidance of sampling over stochastic…

Optimization and Control · Mathematics 2026-04-01 Sebastian Reich

This paper studies mean-field control with joint law dependence under dynamic expectation constraints and/or dynamic state-control-law constraints. We pioneer the establishment of the stochastic maximum principle (SMP) and the derivation of…

Optimization and Control · Mathematics 2026-04-24 Lijun Bo , Jingfei Wang , Xiang Yu

Time change is a powerful technique for generating noises and providing flexible models. In the framework of time changed Brownian and Poisson random measures we study the existence and uniqueness of a solution to a general mean-field…

Probability · Mathematics 2016-08-23 Giulia Di Nunno , Hannes Haferkorn

In this paper, we investigate the optimal control problem for systems driven by mixed fractional Brownian motion (including a fractional Brownian motion with Hurst parameter $H>1/2$ and the standard Brownian motion). By using Malliavin…

Optimization and Control · Mathematics 2024-12-25 Yuhang Li , Yuecai Han

We derive sufficient and necessary optimality conditions in terms of a stochastic maximum principle (SMP) for controls associated with cost functionals of mean-field type, under dynamics driven by a class of Markov chains of mean-field type…

Probability · Mathematics 2018-09-07 Salah Eddine Choutri , Hamidou Tembine

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

In this paper, an open problem is solved, for the stochastic optimal control problem with delay where the control domain is nonconvex and the diffusion term contains both control and its delayed term. Inspired by previous results by \O…

Optimization and Control · Mathematics 2020-07-14 Weijun Meng , Jingtao Shi

In this paper, the Pontryagin-type maximum principle for optimal control of quantum stochastic systems in fermion fields is obtained. These systems have gained significant prominence in numerous quantum applications ranging from physical…

Optimization and Control · Mathematics 2024-06-13 Penghui Wang , Shan Wang

In this paper, we study the stochastic optimal control problem for control system with time-varying delay. The corresponding stochastic differential equation is a kind of stochastic differential delay equation. We prove the existence and…

Optimization and Control · Mathematics 2024-01-17 Yuhang Li , Yuecai Han