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A finite element analysis of a Dirichlet boundary control problem governed by the linear parabolic equation is presented in this article. The Dirichlet control is considered in a closed and convex subset of the energy space $H^1(\Omega…

Numerical Analysis · Mathematics 2021-11-04 Thirupathi Gudi , Gouranga Mallik , Ramesh Ch. Sau

In this paper, we carry out the analysis of the semismooth Newton method for bilinear control problems related to semilinear elliptic PDEs. We prove existence, uniqueness and regularity for the solution of the state equation, as well as…

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

We consider some boundary value tracking optimal control problem constrained by a Neumann boundary value problem for some elliptic partial differential equation where the control acts as right-hand side. This optimal control problem can be…

Numerical Analysis · Mathematics 2026-03-12 Ulrich Langer , Richard Löscher , Olaf Steinbach , Huidong Yang

We study a control-constrained optimal control problem governed by a semilinear elliptic equation. The control acts in a bilinear way on the boundary, and can be interpreted as a heat transfer coefficient. A detailed study of the state…

Optimization and Control · Mathematics 2024-03-06 Eduardo Casas , Konstantinos Chrysafinos , Mariano Mateos

This work establishes a general stochastic maximum principle for partially observed optimal control of semi-linear stochastic partial differential equations in a nonconvex control domain. The state evolves in a Hilbert space driven by a…

Optimization and Control · Mathematics 2025-04-22 Yanzhao Cao , Hongjiang Qian , George Yin

We consider a pointwise tracking optimal control problem for a semilinear elliptic partial differential equation. We derive the existence of optimal solutions and analyze first and, necessary and sufficient, second order optimality…

Numerical Analysis · Mathematics 2021-12-16 Alejandro Allendes , Francisco Fuica , Enrique Otarola

Motivated by various applications, this article develops the notion of boundary control for Maxwell's equations in the frequency domain. Surface curl is shown to be the appropriate regularization in order for the optimal control problem to…

Optimization and Control · Mathematics 2022-10-03 Harbir Antil , Hugo Díaz

This paper is concerned with an optimal control problem governed by a non-smooth semilinear elliptic equation. We show that the control-to-state mapping is directionally differentiable and precisely characterize its Bouligand…

Optimization and Control · Mathematics 2018-01-29 Constantin Christof , Christian Clason , Christian Meyer , Stephan Walther

In this paper, we discuss the numerical approximation of a distributed optimal control problem governed by the von Karman equations, defined in polygonal domains with point-wise control constraints. Conforming finite elements are employed…

Numerical Analysis · Mathematics 2017-09-19 Gouranga Mallik , Neela Nataraj , Jean-Pierre Raymond

We consider finite element solutions to quadratic optimization problems, where the state depends on the control via a well-posed linear partial differential equation. Exploiting the structure of a suitably reduced optimality system, we…

Numerical Analysis · Mathematics 2019-10-03 Fernando Gaspoz , Christian Kreuzer , Andreas Veeser , Winnifried Wollner

Finite element approximations of Dirichlet boundary control problems governed by parabolic PDEs on convex polygonal domains are studied in this paper. The existence of a unique solution to optimal control problems is guaranteed based on…

Optimization and Control · Mathematics 2014-10-02 Wei Gong , Michael Hinze , Zhaojie Zhou

In this article a special class of nonlinear optimal control problems involving a bilinear term in the boundary condition is studied. These kind of problems arise for instance in the identification of an unknown space-dependent Robin…

Numerical Analysis · Mathematics 2024-12-20 Max Winkler

We show that a second order sufficient condition for local optimality, along with a strict complementarity condition, is enough to get the superlinear convergence of the semismooth Newton method for an optimal control problem governed by a…

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

We adopt the integral definition of the fractional Laplace operator and analyze an optimal control problem for a fractional semilinear elliptic partial differential equation (PDE); control constraints are also considered. We establish the…

Numerical Analysis · Mathematics 2021-09-07 Enrique Otarola

This work discusses the finite element discretization of an optimal control problem for the linear wave equation with time-dependent controls of bounded variation. The main focus lies on the convergence analysis of the discretization…

Optimization and Control · Mathematics 2019-07-26 Sebastian Engel , Philip Trautmann , Boris Vexler

In this paper we study optimal control problems governed by a semilinear elliptic equation. The equation is nonmonotone due to the presence of a convection term, despite the monotonocity of the nonlinear term. The resulting operator is…

Optimization and Control · Mathematics 2020-06-11 Eduardo Casas , Mariano Mateos , Arnd Rösch

We investigate $C^1$ finite element methods for one dimensional elliptic distributed optimal control problems with pointwise constraints on the derivative of the state formulated as fourth order variational inequalities for the state…

Numerical Analysis · Mathematics 2020-06-29 Susanne C. Brenner , Li-Yeng Sung , Winnifried Wollner

We consider the finite element discretization and the iterative solution of singularly perturbed elliptic reaction-diffusion equations in three-dimensional computational domains. These equations arise from the optimality conditions for…

Numerical Analysis · Mathematics 2021-02-09 Ulrich Langer , Olaf Steinbach , Huidong Yang

Optimal control problems without control costs in general do not possess solutions due to the lack of coercivity. However, unilateral constraints together with the assumption of existence of strictly positive solutions of a pre-adjoint…

Optimization and Control · Mathematics 2017-02-27 Christian Clason , Anton Schiela

In this paper we propose a new finite element method for solving elliptic optimal control problems with pointwise state constraints, including the distributed controls and the Dirichlet or Neumann boundary controls. The main idea is to use…

Numerical Analysis · Mathematics 2023-06-07 Wei Gong , Zhiyu Tan