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This article examines the Dirichlet boundary control problem governed by the Poisson equation, where the control variables are square integrable functions defined on the boundary of a two-dimensional bounded, convex, polygonal domain. It…

Optimization and Control · Mathematics 2026-04-21 Sudipto Chowdhury , Shallu

Optimal Dirichlet boundary control for a fractional/normal evolution with a final observation is considered. The unique existence of the solution and the first-order optimality condition of the optimal control problem are derived. The…

Numerical Analysis · Mathematics 2020-07-20 Qin Zhou , Binjie Li

We consider an optimal control problem for the steady-state Kirchhoff equation, a prototype for nonlocal partial differential equations, different from fractional powers of closed operators. Existence and uniqueness of solutions of the…

Optimization and Control · Mathematics 2021-12-03 Masoumeh Hashemi , Roland Herzog , Thomas M. Surowiec

In this paper we study we study a Dirichlet optimal control prob- lem associated with a linear elliptic equation the coefficients of which we take as controls in the class of integrable functions. The characteristic feature of this control…

Optimization and Control · Mathematics 2015-10-30 Thierry Horsin , Peter Kogut , Olivier Wilk

In this paper we discuss the numerical solution of elliptic distributed optimal control problems with state or control constraints when the control is considered in the energy norm. As in the unconstrained case we can relate the…

Numerical Analysis · Mathematics 2023-06-28 Peter Gangl , Richard Löscher , Olaf Steinbach

We consider an optimal shape design problem for the plate equation, where the variable thickness of the plate is the design function. This problem can be formulated as a control in the coefficient PDE-constrained optimal control problem…

Optimization and Control · Mathematics 2015-06-11 Klaus Deckelnick , Michael Hinze , Tobias Jordan

Recently the authors have studied a state and control constrained optimal control problem with fractional elliptic PDE as constraints. The goal of this paper is to continue that program forward and introduce an algorithm to solve such…

Optimization and Control · Mathematics 2019-12-12 Harbir Antil , Thomas S. Brown , Deepanshu Verma

We study solution techniques for a linear-quadratic optimal control problem involving fractional powers of elliptic operators. These fractional operators can be realized as the Dirichlet-to-Neumann map for a nonuniformly elliptic problem…

Optimization and Control · Mathematics 2015-04-21 Harbir Antil , Enrique Otarola

This paper analyzes an interface-unfitted numerical method for distributed optimal control problems governed by elliptic interface equations. We follow the variational discretization concept to discretize the optimal control problems, and…

Numerical Analysis · Mathematics 2018-10-05 Tao Wang , Chaochao Yang , Xiaoping Xie

In this paper, we consider a class of time-optimal control problems governed by linear parabolic equations with mixed control-state constraints and end-point constraints, and without Tikhonov regularization term in the objective function.…

Optimization and Control · Mathematics 2025-09-04 Huynh Khanh , Bui Trong Kien

This paper studies an optimal control problem governed by a semilinear elliptic equation, in which the control acts in a multiplicative or bilinear way as the reaction coefficient of the equation. We focus on the numerical discretization of…

Optimization and Control · Mathematics 2025-06-25 Eduardo Casas , Konstantinos Chrysafinos , Mariano Mateos

We consider a linear-quadratic elliptic optimal control problem with point evaluations of the state variable in the cost functional. The state variable is discretized by conforming linear finite elements. For control discretization, three…

Numerical Analysis · Mathematics 2018-02-09 Niklas Behringer , Dominik Meidner , Boris Vexler

We present the Dirichlet-Neumann (DN) and Neumann-Neumann (NN) methods applied to the optimal control problems arising from elliptic partial differential equations (PDEs) under the $H^{-1}$ regularization. We use the Lagrange multiplier…

Numerical Analysis · Mathematics 2023-08-25 Martin Jakob Gander , Liu-Di Lu

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

This paper introduces a new variational formulation for Dirichlet boundary control problem of elliptic partial differential equations, based on observations that the state and adjoint state are related through the control on the boundary of…

Numerical Analysis · Mathematics 2019-04-23 Shaohong Du , Zhiqiang Cai

In this paper we consider the convergence analysis of adaptive finite element method for elliptic optimal control problems with pointwise control constraints. We use variational discretization concept to discretize the control variable and…

Numerical Analysis · Mathematics 2016-08-31 Wei Gong , Ningning Yan

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

We adopt the integral definition of the fractional Laplace operator and study an optimal control problem on Lipschitz domains that involves a fractional elliptic partial differential equation (PDE) as state equation and a control variable…

Numerical Analysis · Mathematics 2024-02-14 Francisco Bersetche , Francisco Fuica , Enrique Otarola , Daniel Quero

A numerical method is proposed for a class of stochastic control problems including singular behavior. This method solves an infinite-dimensional linear program equivalent to the stochastic control problem using a finite element type…

Probability · Mathematics 2018-06-11 Martin G. Vieten , Richard H. Stockbridge

An optimal control problem driven by an ordinary differential equation under continuous state constraints is considered in this study. From an operational point of view, we introduce a discrete state constraints optimal control problem and…

Optimization and Control · Mathematics 2018-12-04 Shuzhen Yang