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A numerical study of an optimal control formulation for a shape optimization problem governed by an elliptic variational inequality is performed. The shape optimization problem is reformulated as a boundary control problem in a fixed…

Optimization and Control · Mathematics 2018-01-22 Raino A. E. Mäkinen

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

This paper develops numerical methods for optimal control of mechanical systems in the Lagrangian setting. It extends the theory of discrete mechanics to enable the solutions of optimal control problems through the discretization of…

Optimization and Control · Mathematics 2015-06-04 Fernando Jimenez , Marin Kobilarov , David Martin de Diego

This paper aims to study the convergence of adaptive finite element method for control constrained elliptic optimal control problems under $L^2$-norm. We prove the contraction property and quasi-optimal complexity for the $L^2$-norm errors…

Numerical Analysis · Mathematics 2016-11-16 Wei Gong , Ningning Yan , Zhaojie Zhou

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 2024-02-12 Sudipto Chowdhury , Divay Garg

We consider an optimal control problem $\cQ$ governed by an elliptic quasivariational inequality with unilateral constraints. The existence of optimal pairs of the problem is a well known result, see \cite{SS}, for instance. We associate to…

Optimization and Control · Mathematics 2020-05-26 Mircea Sofonea , Domingo A. Tarzia

This work addresses an optimal control problem for a semilinear elliptic equation in two-dimensional space, characterized by an exponential nonlinearity and a singular source term. The source is modeled as a finite linear combination of…

Optimization and Control · Mathematics 2025-05-28 Vu Huu Nhu

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

We consider an optimal control problem for the obstacle problem with an elliptic variational inequality. The obstacle function which is the control function is assumed in $H^{2}$. We use an approximate technique to introduce a family of…

Optimization and Control · Mathematics 2008-12-18 Radouen Ghanem

We propose and analyze a monotone finite element method for an elliptic distributed optimal control problem constrained by a convection-diffusion-reaction equation in the convection-dominated regime. The method is based on the edge-averaged…

Numerical Analysis · Mathematics 2025-11-04 SeongHee Jeong , Seulip Lee , Sijing Liu

In this paper, we investigate optimal control problems governed by semilinear elliptic variational inequalities involving constraints on the state, and more precisely the obstacle problem. Since we adopt a numerical point of view, we first…

Optimization and Control · Mathematics 2020-07-10 El Hassene Osmani , Mounir Haddou , Naceurdine Bensalem

In this paper we study an optimal control problem associated to a linear degenerate elliptic equation with mixed boundary conditions. The equations of this type can exhibit the Lavrentieff phenomenon and non-uniqueness of weak solutions. We…

Optimization and Control · Mathematics 2010-12-16 Giuseppe Buttazzo , Peter I. Kogut

We analyze space-time finite element methods for the numerical solution of distributed parabolic optimal control problems with energy regularization in the Bochner space $L^2(0,T;H^{-1}(\Omega))$. By duality, the related norm can be…

Numerical Analysis · Mathematics 2020-04-22 Ulrich Langer , Olaf Steinbach , Fredi Tröltzsch , Huidong Yang

We discuss several optimization procedures to solve finite element approximations of linear-quadratic Dirichlet optimal control problems governed by an elliptic partial differential equation posed on a 2D or 3D Lipschitz domain. The control…

Optimization and Control · Mathematics 2019-01-25 Mariano Mateos

We study the numerical approximation of linear-quadratic optimal control problems subject to the fractional Laplace equation with its spectral definition. We compute an approximation of the state equation using a discretization of the…

Numerical Analysis · Mathematics 2018-09-28 Stefan Dohr , Christian Kahle , Sergejs Rogovs , Piotr Swierczynski

We consider a parabolic optimal control problem with an initial measure control. The cost functional consists of a tracking term corresponding to the observation of the state at final time. Instead of a regularization term in the cost…

Optimization and Control · Mathematics 2020-08-18 Evelyn Herberg , Michael Hinze

We consider a linear-quadratic optimization problem with pointwise bounds on the state for which the constraint is given by the Laplace-Beltrami equation (to have uniqueness we add an lower order term) on a two-dimensional surface . By…

Optimization and Control · Mathematics 2016-06-10 Ahmad Ahmad Ali , Michael Hinze , Heiko Kröner

In this paper we consider optimal control problems where the control variable is a potential and the state equation is an elliptic partial differential equation of a Schr\"odinger type, governed by the Laplace operator. The cost functional…

Optimization and Control · Mathematics 2023-02-07 Giuseppe Buttazzo , Juan Casado_Díaz , Faustino Maestre

In this work, we investigate optimal control of a Brinkman equation couple with sixth-order Cahn-Hilliard equation. The Cahn-Hilliard equation is endowed with a source term accounting for mass exchange and the velocity equation contains a…

Optimization and Control · Mathematics 2025-12-09 Manika Bag

This paper investigates a symmetric dual-wind discontinuous Galerkin (DWDG) method for solving an elliptic optimal control problem with control constraints. The governing constraint is an elliptic partial differential equation (PDE), which…

Numerical Analysis · Mathematics 2025-06-17 Satyajith Bommana Boyana , Thomas Lewis , Sijing Liu , Yi Zhang