English
Related papers

Related papers: Relationships Between the Maximum Principle and Dy…

200 papers

In this paper, we study the relationship between maximum principle (MP) and dynamic programming principle (DPP) for stochastic recursive optimal control problem driven by $G$-Brownian motion. Under the smooth assumption for the value…

Optimization and Control · Mathematics 2022-10-12 Xiaojuan Li

In this paper, we study a stochastic recursive optimal control problem in which the value functional is defined by the solution of a backward stochastic differential equation (BSDE) under $\tilde{G}$-expectation. Under standard assumptions,…

Optimization and Control · Mathematics 2021-06-08 Mingshang Hu , Shaolin Ji , Xiaojuan Li

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

We discuss a mathematical framework for analysis of optimal control problems on infinite-dimensional manifolds. Such problems arise in study of optimization for partial differential equations with some symmetry. It is shown that some…

Optimization and Control · Mathematics 2014-05-19 Robert J. Kipka , Yuri S. Ledyaev

The paper concerns the study of the Pontryagin Maximum Principle for an infinite dimensional and infinite horizon boundary control problem for linear partial differential equations. The optimal control model has already been studied both in…

Optimization and Control · Mathematics 2007-11-26 Silvia Faggian

For a class of path-dependent stochastic evolution equations driven by cylindrical $Q$-Wiener process, we study the Pontryagin's maximum principle for the stochastic recursive optimal control problem. In this infinite-dimensional control…

Optimization and Control · Mathematics 2025-11-07 Guomin Liu , Jian Song , Meng Wang

We study the properties of the value function associated with an optimal control problem with uncertainties, known as average or Riemann-Stieltjes problem. Uncertainties are assumed to belong to a compact metric probability space, and…

Optimization and Control · Mathematics 2024-07-19 M. Soledad Aronna , Michele Palladino , Oscar Sierra

This work introduces a sequential convex programming framework for non-linear, finite-dimensional stochastic optimal control, where uncertainties are modeled by a multidimensional Wiener process. We prove that any accumulation point of the…

Optimization and Control · Mathematics 2022-09-27 Riccardo Bonalli , Thomas Lew , Marco Pavone

We study a continuous time stochastic optimal control problem under partial observations that are available only at discrete time instants. This hybrid setting, with continuous dynamics and intermittent noisy measurements, arises in…

Optimization and Control · Mathematics 2026-01-01 Christian Bayer , Saifeddine Ben naamia , Erik von Schwerin , Raul Tempone

We obtain the dynamic programming equations and optimality conditions akin to Pontryagin's extremum principle for certain mathematical models of hybrid control systems.

Optimization and Control · Mathematics 2007-05-23 S. A. Belbas

We consider the approximation of some optimal control problems for the Navier-Stokes equation via a Dynamic Programming approach. These control problems arise in many industrial applications and are very challenging from the numerical point…

Optimization and Control · Mathematics 2022-07-18 Maurizio Falcone , Gerhard Kirsten , Luca Saluzzi

We prove a version of the stochastic maximum principle, in the sense of Pontryagin, for the finite horizon optimal control of a stochastic partial differential equation driven by an infinite dimensional additive noise. In particular we…

Probability · Mathematics 2017-03-14 Marco Fuhrman , Carlo Orrieri

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

In this paper, we consider a class of stochastic control problems for stochastic differential equations with random coefficients. The control domain need not to be convex but the control process is not allowed to enter in diffusion term.…

Optimization and Control · Mathematics 2020-08-06 Ishak Alia , Mohamed Sofiane Alia

The continuous dynamical system approach to deep learning is explored in order to devise alternative frameworks for training algorithms. Training is recast as a control problem and this allows us to formulate necessary optimality conditions…

Machine Learning · Computer Science 2018-06-05 Qianxiao Li , Long Chen , Cheng Tai , Weinan E

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

We prove a version of the maximum principle, in the sense of Pontryagin, for the optimal control of a stochastic partial differential equation driven by a finite dimensional Wiener process. The equation is formulated in a semi-abstract form…

Optimization and Control · Mathematics 2013-02-05 Marco Fuhrman , Ying Hu , Gianmario Tessitore

This paper is concerned with a partially observed hybrid optimal control problem, where continuous dynamics and discrete events coexist and in particular, the continuous dynamics can be observed while the discrete events, described by a…

Optimization and Control · Mathematics 2023-03-14 Siyu Lv , Jie Xiong , Wen Xu

Without exact knowledge of the true system dynamics, optimal control of non-linear continuous-time systems requires careful treatment under epistemic uncertainty. In this work, we translate a probabilistic interpretation of the Pontryagin…

Machine Learning · Computer Science 2025-09-03 David Leeftink , Çağatay Yıldız , Steffen Ridderbusch , Max Hinne , Marcel van Gerven

Model predictive control offers a powerful framework for managing constrained systems, but its repeated online optimization can become computationally prohibitive. Multiparametric programming addresses this challenge by precomputing optimal…

Optimization and Control · Mathematics 2026-03-19 Lida Lamakani , Efstratios N. Pistikopoulos