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The purpose of this work is to study an optimal control problem for a semilinear elliptic partial differential equation with a linear combination of Dirac measures as a forcing term; the control variable corresponds to the amplitude of such…

Optimization and Control · Mathematics 2023-07-04 Enrique Otarola

This paper deals with generalized differentiability and second-order necessary optimality conditions for a box-constrained optimal control problem governed by an exponential semilinear elliptic equation with discrete measures as sources,…

Optimization and Control · Mathematics 2026-05-20 Vu Huu Nhu , Nguyen Hai Son , Phan Quang Sang , Tran Duy

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

An optimal control problem for a semilinear elliptic equation of divergence form is considered. Both the leading term and the semilinear term of the state equation contain the control. The well-known Pontryagin type maximum principle for…

Optimization and Control · Mathematics 2017-03-28 Hongwei Lou , Jiongmin Yong

We consider a one dimensional elliptic distributed optimal control problem with pointwise constraints on the derivative of the state. By exploiting the variational inequality satisfied by the derivative of the optimal state, we obtain…

Numerical Analysis · Mathematics 2021-06-18 Susanne C. Brenner , Li-yeng Sung , Winnifried Wollner

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

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 investigate optimal control problems governed by the elliptic partial differential equation $-\Delta u=f$ subject to Dirichlet boundary conditions on a given domain $\Omega$. The control variable in this setting is the right-hand side…

Optimization and Control · Mathematics 2025-09-03 Giuseppe Buttazzo , Juan Casado-Díaz , Faustino Maestre

In this paper, we study optimal control problems of semilinear elliptic and parabolic equations. A tracking cost functional, quadratic in the control and state variables, is considered. No control constraints are imposed. We prove that the…

Optimization and Control · Mathematics 2022-10-21 Eduardo Casas , Daniel Wachsmuth

This work is concerned with an optimal control problem governed by a non-smooth quasilinear elliptic equation with a nonlinear coefficient in the principal part that is locally Lipschitz continuous and directionally but not G\^ateaux…

Optimization and Control · Mathematics 2021-09-28 Christian Clason , Vu Huu Nhu , Arnd Rösch

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

We consider an optimal control problem governed by an elliptic variational inequality of the second kind. The problem is discretized by linear finite elements for the state and a variational discrete approach for the control. Based on a…

Numerical Analysis · Mathematics 2020-11-25 Christian Meyer , Monika Weymuth

This paper is concerned with the analysis of a class of optimal control problems governed by a time-harmonic eddy current system with a dipole source, which is taken as the control variable. A mathematical model is set up for the state…

Optimization and Control · Mathematics 2019-12-04 Gabriele Caselli

We consider a stochastic control problem where the set of strict (classical) controls is not necessarily convex and the the variable control has two components, the first being absolutely continuous and the second singular. The system is…

Probability · Mathematics 2008-12-20 Seid Bahlali

We consider an elliptic optimal control problem where the objective functional contains evaluations of the state at a finite number of points. In particular, we use a fidelity term that encourages the state to take certain values at these…

Numerical Analysis · Mathematics 2014-11-19 C. Brett , A. S. Dedner , C. M. Elliott

In this paper, we carry out the numerical analysis of a nonsmooth quasilinear elliptic optimal control problem, where the coefficient in the divergence term of the corresponding state equation is not differentiable with respect to the state…

Numerical Analysis · Mathematics 2024-02-23 Christian Clason , Vu Huu Nhu , Arnd Rösch

The article examines a linear-quadratic Neumann control problem that is governed by a non-coercive elliptic equation. Due to the non-self-adjoint nature of the linear control-to-state operator, it is necessary to independently study both…

Optimization and Control · Mathematics 2025-06-25 Thomas Apel , Mariano Mateos , Arnd Rösch

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

In this paper, an optimal control problem governed by a class of p-Laplacian elliptic equations is studied. In particular, as no monotonicity assumption is assumed on the nonlinear term, the state equation may admit several solutions for…

Optimization and Control · Mathematics 2019-08-28 Hongwei Lou , Shu Luan

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
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