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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 a class of infinite-dimensional optimization problems in which a distributed vector-valued variable should pointwise almost everywhere take values from a given finite set $\mathcal{M}\subset\mathbb{R}^m$. Such hybrid…

Optimization and Control · Mathematics 2021-11-09 Christian Clason , Carla Tameling , Benedikt Wirth

We consider the variational discretization of a linear-quadratic optimal control problem with pointwise control and state constraints. In order to allow for a Fr\'echet smooth norm, the problem is reformulated by means of a reflexive…

Optimization and Control · Mathematics 2010-08-24 Morten Vierling

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 consider a general optimization problem of minimizing a composite objective functional defined over a class of probability distributions. The objective is composed of two functionals: one is assumed to possess the variational…

Machine Learning · Computer Science 2024-08-20 Dai Hai Nguyen , Tetsuya Sakurai

We derive a-priori error estimates for the finite-element approximation of a distributed optimal control problem governed by the steady one-dimensional Burgers equation with pointwise box constraints on the control. Here the approximation…

Optimization and Control · Mathematics 2014-11-18 Pedro Martín Merino Rosero

The paper is concerned with an optimal control problem governed by the rate-independent system of quasi-static perfect elasto-plasticity. The objective is optimize the displacement field in the domain occupied by the body by means of…

Optimization and Control · Mathematics 2020-03-24 Christian Meyer , Stephan Walther

We consider a control-constrained parabolic optimal control problem without Tikhonov term in the tracking functional. For the numerical treatment, we use variational discretization of its Tikhonov regularization: For the state and the…

Optimization and Control · Mathematics 2017-12-08 Nikolaus von Daniels , Michael Hinze

We propose an algorithm to solve optimization problems constrained by partial (ordinary) differential equations under uncertainty, with almost sure constraints on the state variable. To alleviate the computational burden of high-dimensional…

Optimization and Control · Mathematics 2024-07-08 Harbir Antil , Sergey Dolgov , Akwum Onwunta

We consider bilinear optimal control problems, whose objective functionals do not depend on the controls. Hence, bang-bang solutions will appear. We investigate sufficient second-order conditions for bang-bang controls, which guarantee…

Optimization and Control · Mathematics 2017-07-24 Eduardo Casas , Daniel Wachsmuth , Gerd Wachsmuth

We consider a class of (ill-posed) optimal control problems in which a distributed vector-valued control is enforced to pointwise take values in a finite set $\mathcal{M}\subset\mathbb{R}^m$. After convex relaxation, one obtains a…

Optimization and Control · Mathematics 2018-06-28 Christian Clason , Carla Tameling , Benedikt Wirth

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

This paper considers optimal control of fractional parabolic PDEs with both state and control constraints. The key challenge is how to handle the state constraints. Similarly, to the elliptic case, in this paper, we establish several new…

Analysis of PDEs · Mathematics 2020-04-22 Harbir Antil , Thomas S. Brown , Deepanshu Verma , Mahamadi Warma

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

This paper addresses a new class of optimal control problems for perturbed sweeping processes with measurable controls in additive perturbations of the dynamics and smooth controls in polyhedral moving sets. We develop a constructive…

Optimization and Control · Mathematics 2020-02-14 Tan H. Cao , Giovanni Colombo , Boris S. Mordukhovich , Dao Nguyen

We study an optimal control problem in which both the objective function and the dynamic constraint contain an uncertain parameter. Since the distribution of this uncertain parameter is not exactly known, the objective function is taken as…

Optimization and Control · Mathematics 2016-11-29 Jianxiong Ye , Lei Wang , Changzhi Wu , Jie Sun , Kok Lay Teo , Xiangyu Wang

The aim of this work is to derive a priori error estimates for finite element discretizations of control--constrained optimal control problems that involve the Stokes system and Dirac measures. The first problem entails the minimization of…

Numerical Analysis · Mathematics 2020-04-29 Francisco Fuica , Enrique Otarola , Daniel Quero

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

In [1] we consider an optimal control problem subject to a semilinear elliptic PDE together with its variational discretization, where we provide a condition which allows to decide whether a solution of the necessary first order conditions…

Optimization and Control · Mathematics 2017-05-04 Ahmad Ahmad Ali , Klaus Deckelnick , Michael Hinze

In this paper, the optimal strong error estimates for stochastic parabolic optimal control problem with additive noise and integral state constraint are derived based on time-implicit and finite element discretization. The continuous and…

Optimization and Control · Mathematics 2025-05-13 Qiming Wang , Wanfang Shen , Wenbin Liu