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This study focuses on using direct methods (first-discretize-then-optimize) to solve optimal control problems for a class of nonsmooth dynamical systems governed by differential variational inequalities (DVI), called optimal control…

Optimization and Control · Mathematics 2025-12-04 Kangyu Lin , Toshiyuki Ohtsuka

In this paper, a gradient-free distributed algorithm is introduced to solve a set constrained optimization problem under a directed communication network. Specifically, at each time-step, the agents locally compute a so-called…

Optimization and Control · Mathematics 2021-09-06 Yipeng Pang , Guoqiang Hu

This paper studies an infinite horizon optimal control problem for discrete-time linear system and quadratic criteria, both with random parameters which are independent and identically distributed with respect to time. In this general…

Optimization and Control · Mathematics 2024-03-04 Deyue Li

This paper applies the gradient discretisation method (GDM) for fourth order elliptic variational inequalities. The GDM provides a new formulation of error estimates and a complete convergence analysis of several numerical methods. We show…

Numerical Analysis · Mathematics 2023-05-31 Yahya Alnashri

In this paper, we consider the finite element approximation to a parabolic Dirichlet boundary control problem and establish new a priori error estimates. In the temporal semi-discretization we apply the DG(0) method for the state and the…

Numerical Analysis · Mathematics 2023-06-29 Dongdong Liang , Wei Gong , Xiaoping Xie

Retractions maps are used to define a discretization of the tangent bundle of the configuration manifold as two copies of the configuration manifold where the dynamics take place. Such discretization maps can be conveniently lifted to the…

Optimization and Control · Mathematics 2022-03-03 María Barbero Liñán , David Martín de Diego

The ability to differentiate through optimization problems has unlocked numerous applications, from optimization-based layers in machine learning models to complex design problems formulated as bilevel programs. It has been shown that…

Optimization and Control · Mathematics 2024-03-05 Lucas Fuentes Valenzuela , Robin Brown , Marco Pavone

This paper presents computational analysis of the inverse Stefan type free boundary problem, where information on the boundary heat flux is missing and must be found along with the temperature and the free boundary. We pursue optimal…

Optimization and Control · Mathematics 2018-07-24 Ugur G. Abdulla , Vladislav Bukshtynov , Ali Hagverdiyev

This paper concerns the numerical procedure for solving hybrid optimal control problems with sliding modes. The proposed procedure has several features which distinguishes it from the other procedures for the problem. First of all a sliding…

Optimization and Control · Mathematics 2021-01-18 Radoslaw Pytlak , Damian Suski

We review basic design principles underpinning the construction of mimetic finite difference and a few finite volume and finite element schemes for mixed formulations of elliptic problems. For a class of low-order mixed-hybrid schemes, we…

Numerical Analysis · Mathematics 2016-10-20 Konstantin Lipnikov , Gianmarco Manzini

This article provides quasi-optimal a priori error estimates for an optimal control problem constrained by an elliptic obstacle problem where the finite element discretization is carried out using the symmetric interior penalty…

Numerical Analysis · Mathematics 2023-12-21 Harbir Antil , Rohit Khandelwal , Umarkhon Rakhimov

In this work, we present an efficient gradient projection method for solving a class of stochastic optimal control problem with expected integral state constraint. The first order optimality condition system consisting of forward-backward…

Optimization and Control · Mathematics 2024-12-24 Qiming Wang , Wenbin Liu

The aim of this work is to derive a priori error estimates for finite element discretizations of control--constrained optimal control problems that involve the Stokes system and Dirac measures. The first problem entails the minimization of…

Numerical Analysis · Mathematics 2020-04-29 Francisco Fuica , Enrique Otarola , Daniel Quero

We consider an optimal control problem on a bounded domain $\Omega\subset\mathbb{R}^2,$ governed by a parabolic convection--diffusion--reaction equation with pointwise control constraints. We follow the optimize--then--discretize approach,…

Numerical Analysis · Mathematics 2025-12-11 Christos Pervolianakis

A continuous optimal control problem governed by an elliptic variational inequality was considered in Boukrouche-Tarzia, Comput. Optim. Appl., 53 (2012), 375-392 where the control variable is the internal energy $g$. It was proved the…

Numerical Analysis · Mathematics 2015-05-18 Mariela Olguín , Domingo A. Tarzia

In this paper, we propose a class of discrete-time approximation schemes for stochastic optimal control problems under the $G$-expectation framework. The proposed schemes are constructed recursively based on piecewise constant policy. We…

Optimization and Control · Mathematics 2021-10-05 Lianzi Jiang

We introduce a max-plus analogue of the Petrov-Galerkin finite element method to solve finite horizon deterministic optimal control problems. The method relies on a max-plus variational formulation. We show that the error in the sup norm…

Optimization and Control · Mathematics 2009-12-13 Marianne Akian , Stephane Gaubert , Asma Lakhoua

We consider policy gradient methods for stochastic optimal control problem in continuous time. In particular, we analyze the gradient flow for the control, viewed as a continuous time limit of the policy gradient method. We prove the global…

Optimization and Control · Mathematics 2025-04-15 Mo Zhou , Jianfeng Lu

Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…

Optimization and Control · Mathematics 2019-10-29 Sulaiman A. Alghunaim , Kun Yuan , Ali H. Sayed

This paper proposes an algorithmic technique for a class of optimal control problems where it is easy to compute a pointwise minimizer of the Hamiltonian associated with every applied control. The algorithm operates in the space of relaxed…

Optimization and Control · Mathematics 2016-03-10 M. T. Hale , Y. Wardi , H. Jaleel , M. Egerstedt