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In this paper we consider a parabolic optimal control problem with a Dirac type control with moving point source in two space dimensions. We discretize the problem with piecewise constant functions in time and continuous piecewise linear…

Numerical Analysis · Mathematics 2018-08-17 Dmitriy Leykekhman , Boris Vexler

In many problems in optimal control, one seeks to minimise an objective function subject to constraints on the velocity of the system. Imposing these constraints directly -- the ``hard-constrained'' approach -- is often analytically and…

Optimization and Control · Mathematics 2026-04-27 Rufus Lawrence , Aleš Wodecki , Johannes Aspman , Jakub Mareček

We consider a linear-quadratic elliptic optimal control problem with point evaluations of the state variable in the cost functional. The state variable is discretized by conforming linear finite elements. For control discretization, three…

Numerical Analysis · Mathematics 2018-02-09 Niklas Behringer , Dominik Meidner , Boris Vexler

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

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 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

Optimization problems with $L^1$-control cost functional subject to an elliptic partial differential equation (PDE) are considered. However, different from the finite dimensional $l^1$-regularization optimization, the resulting discretized…

Optimization and Control · Mathematics 2017-09-28 Xiaoliang Song , Bo Chen , Bo Yu

In this paper, elliptic control problems with integral constraint on the gradient of the state and box constraints on the control are considered. The optimal conditions of the problem are proved. To numerically solve the problem, we use the…

Optimization and Control · Mathematics 2018-10-05 Zixuan Chen , Xiaoliang Song , Bo Yu , Xiaotong Chen

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

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 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 optimal control of a mechanical system is of crucial importance in many realms. Typical examples are the determination of a time-minimal path in vehicle dynamics, a minimal energy trajectory in space mission design, or optimal motion…

Optimization and Control · Mathematics 2008-10-09 S. Ober-Bloebaum , O. Junge , J. E. Marsden

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

This work addresses an optimal control problem constrained by a degenerate kinetic equation of parabolic-hyperbolic type. Using a hypocoercivity framework we establish the well-posedness of the problem and demonstrate that the optimal…

Numerical Analysis · Mathematics 2024-12-17 Aaron Pim , Tristan Pryer , Alex Trenam

This paper is concerned with second-order optimality conditions for Tikhonov regularized optimal control problems governed by the obstacle problem. Using a simple observation that allows to characterize the structure of optimal controls on…

Optimization and Control · Mathematics 2019-06-24 Constantin Christof , Gerd Wachsmuth

We derive a framework to compute optimal controls for problems with states in the space of probability measures. Since many optimal control problems constrained by a system of ordinary differential equations (ODE) modelling interacting…

Optimization and Control · Mathematics 2020-09-23 Martin Burger , René Pinnau , Claudia Totzeck , Oliver Tse

In this paper we study the mixed virtual element approximation to an elliptic optimal control problem with boundary observations. The objective functional of this type of optimal control problem contains the outward normal derivatives of…

Numerical Analysis · Mathematics 2023-12-19 Minghui Yang , Zhaojie Zhou

In this paper we study an optimal control problem (OCP) associated to a linear elliptic equation {on a bounded domain $\Omega$}. The matrix-valued coefficients A of such systems is our control taken in L2 which in particular may comprise…

Optimization and Control · Mathematics 2013-06-12 Thierry Horsin , Peter I. Kogut

We construct an efficient numerical scheme for solving obstacle problems in divergence form. The numerical method is based on a reformulation of the obstacle in terms of an L1-like penalty on the variational problem. The reformulation is an…

Numerical Analysis · Mathematics 2014-04-08 Giang Tran , Hayden Schaeffer , William M. Feldman , Stanley J. Osher

Space-time finite element discretizations of time-optimal control problems governed by linear parabolic PDEs and subject to pointwise control constraints are considered. Optimal a priori error estimates are obtained for the control variable…

Optimization and Control · Mathematics 2018-09-14 Lucas Bonifacius , Konstantin Pieper , Boris Vexler