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In this paper, a class of semilinear fractional elliptic equations associated to the spectral fractional Dirichlet Laplace operator is considered. We establish the existence of optimal solutions as well as a minimum principle of Pontryagin…

Optimization and Control · Mathematics 2023-04-28 Cyrille Kenne , Gisèle Mophou , Mahamadi Warma

The classical arguments employed when obtaining error estimates of Finite Element (FE) discretisations of elliptic problems lead to more restrictive assumptions on the regularity of the exact solution when applied to non-conforming methods.…

Numerical Analysis · Mathematics 2024-11-25 J. Blechta , P. A. Gazca-Orozco , A. Kaltenbach , M. Růžička

We devise and analyze a reliable and efficient a posteriori error estimator for a semilinear control-constrained optimal control problem in two and three dimensional Lipschitz, but not necessarily convex, polytopal domains. We consider a…

Numerical Analysis · Mathematics 2019-11-22 Alejandro Allendes , Francisco Fuica , Enrique Otarola , Daniel Quero

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

The paper is devoted to the study of a new class of optimal control problems governed by discontinuous constrained differential inclusions of the sweeping type with involving the duration of the dynamic process into optimization. We develop…

Optimization and Control · Mathematics 2023-10-18 Giovanni Colombo , Boris S. Mordukhovich , Dao Nguyen , Trang Nguyen

We propose an a posteriori error estimator for a sparse optimal control problem: the control variable lies in the space of regular Borel measures. We consider a solution technique that relies on the discretization of the control variable as…

Numerical Analysis · Mathematics 2018-06-14 Francisco Fuica , Enrique Otarola , Abner J. Salgado

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 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

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 work focuses on numerical solutions of optimal control problems. A time discretization error representation is derived for the approximation of the associated value function. It concerns Symplectic Euler solutions of the Hamiltonian…

Optimization and Control · Mathematics 2016-02-23 Jesper Karlsson , Stig Larsson , Mattias Sandberg , Anders Szepessy , Raùl Tempone

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

In this paper, we discuss optimality conditions for optimization problems involving random state constraints, which are modeled in probabilistic or almost sure form. While the latter can be understood as the limiting case of the former, the…

Optimization and Control · Mathematics 2024-01-17 Caroline Geiersbach , René Henrion

In this paper error analysis for finite element discretizations of Dirichlet boundary control problems is developed. For the first time, optimal discretization error estimates are established in the case of three dimensional polyhedral and…

Numerical Analysis · Mathematics 2024-01-05 Johannes Pfefferer , Boris Vexler

We propose and analyze a new discretization technique for a linear-quadratic optimal control problem involving the fractional powers of a symmetric and uniformly elliptic second oder operator; control constraints are considered. Since these…

Numerical Analysis · Mathematics 2016-07-08 Enrique Otarola

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

A counterexample to uniqueness of global minimizers of semilinear optimal control problems is given. The lack of uniqueness occurs for a special choice of the state-target in the cost functional. Our arguments show also that, for some…

Optimization and Control · Mathematics 2020-12-29 Dario Pighin

We propose and analyze a posteriori error estimators for an optimal control problem that involves an elliptic partial differential equation as state equation and a control variable that enters the state equation as a coefficient; pointwise…

Optimization and Control · Mathematics 2022-03-31 Francisco Fuica , Enrique Otarola

A semilinear initial-boundary value problem with a Caputo time derivative of fractional order $\alpha\in(0,1)$ is considered, solutions of which typically exhibit a singular behaviour at an initial time. For L1-type discretizations of this…

Numerical Analysis · Mathematics 2022-08-12 Natalia Kopteva

It has been recently established that a deterministic infinite horizon discounted optimal control problem in discrete time is closely related to a certain infinite dimensional linear programming problem and its dual. In the present paper,…

Optimization and Control · Mathematics 2018-02-19 Vladimir Gaitsgory , Alex Parkinson , Ilya Shvartsman

A continuous optimal control problem governed by an elliptic variational inequality was considered in Boukrouche-Tarzia, Comput. Optim. Appl., 53 (2012), 375-392 where the control variable is the internal energy $g$. It was proved the…

Numerical Analysis · Mathematics 2015-05-18 Mariela Olguín , Domingo A. Tarzia