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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

This note is concerned with an optimal control problem governed by the relativistic Maxwell-Newton-Lorentz equations, which describes the motion of charges particles in electro-magnetic fields and consists of a hyperbolic PDE system coupled…

Optimization and Control · Mathematics 2014-11-27 C. Meyer , S. M. Schnepp , O. Thoma

This paper is concerned with the discretization error analysis of semilinear Neumann boundary control problems in polygonal domains with pointwise inequality constraints on the control. The approximations of the control are piecewise…

Numerical Analysis · Mathematics 2015-05-12 Johannes Pfefferer , Klaus Krumbiegel

This paper is concerned with finite element error estimates for Neumann boundary control problems posed on convex and polyhedral domains. Different discretization concepts are considered and for each optimal discretization error estimates…

Numerical Analysis · Mathematics 2024-09-18 Johannes Pfefferer , Boris Vexler

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 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

In this paper, we investigate optimal control problems subject to a semilinear elliptic partial differential equations. The cost functional contains a term that measures the size of the support of the control, which is the so-called…

Optimization and Control · Mathematics 2020-02-13 Eduardo Casas , Daniel Wachsmuth

In this work, we investigate a neural network based solver for optimal control problems (without / with box constraint) for linear and semilinear second-order elliptic problems. It utilizes a coupled system derived from the first-order…

Optimization and Control · Mathematics 2024-05-09 Yongcheng Dai , Bangti Jin , Ramesh Sau , Zhi Zhou

We investigate the properties of certain elliptic systems leading, a~priori, to solutions that belong to the space of Radon measures. We show that if the problem is equipped with a so-called asymptotic Uhlenbeck structure, then the solution…

Analysis of PDEs · Mathematics 2017-05-24 Lisa Beck , Miroslav Bulíček , Josef Málek , Endre Süli

An optimal control problem on finite-dimensional positive cones is stated. Under a critical assumption on the cone, the corresponding Bellman equation is satisfied by a linear function, which can be computed by convex optimization. A…

Optimization and Control · Mathematics 2024-10-02 Richard Pates , Anders Rantzer

In this paper, we investigate optimal control problems for Allen-Cahn equations with singular nonlinearities and a dynamic boundary condition involving singular nonlinearities and the Laplace-Beltrami operator. The approach covers both the…

Analysis of PDEs · Mathematics 2014-10-27 Pierluigi Colli , Jürgen Sprekels

We present a method to solve a special class of parameter identification problems for an elliptic optimal control problem to global optimality. The bilevel problem is reformulated via the optimal-value function of the lower-level problem.…

Optimization and Control · Mathematics 2022-03-02 Markus Friedemann , Felix Harder , Gerd Wachsmuth

The numerical analysis of a family of distributed mixed optimal control problems governed by elliptic variational inequalities (with parameter $\alpha >0$) is obtained through the finite element method when its parameter $h\rightarrow 0$.…

Numerical Analysis · Mathematics 2016-01-05 Mariela C. Olguin , Domingo A. Tarzia

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

We discretize a risk-neutral optimal control problem governed by a linear elliptic partial differential equation with random inputs using a Monte Carlo sample-based approximation and a finite element discretization, yielding finite…

Optimization and Control · Mathematics 2023-11-10 Johannes Milz

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

This work investigates an elliptic optimal control problem defined on uncertain domains and discretized by a fictitious domain finite element method and cut elements. Key ingredients of the study are to manage cases considering the usually…

Numerical Analysis · Mathematics 2022-04-06 Aikaterini Aretaki , Efthymios N. Karatzas

An optimal control problem for the linear wave equation with control cost chosen as the BV semi-norm in time is analyzed. This formulation enhances piecewise constant optimal controls and penalizes the number of jumps. Existence of optimal…

Optimization and Control · Mathematics 2018-09-11 Sebastian Engel , Karl Kunisch

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

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