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We propose a mean-field optimal control problem for the parameter identification of a given pattern. The cost functional is based on the Wasserstein distance between the probability measures of the modeled and the desired patterns. The…

Optimization and Control · Mathematics 2021-04-08 Martin Burger , Lisa Maria Kreusser , Claudia Totzeck

We consider variational discretization of a parabolic optimal control problem governed by space-time measure controls. For the state discretization we use a Petrov-Galerkin method employing piecewise constant states and piecewise linear and…

Optimization and Control · Mathematics 2019-11-25 Evelyn Herberg , Michael Hinze , Henrik Schumacher

In this paper we present a new steepest-descent type algorithm for convex optimization problems. Our algorithm pieces the unknown into sub-blocs of unknowns and considers a partial optimization over each sub-bloc. In quadratic optimization,…

Optimization and Control · Mathematics 2015-01-15 Mohamed Kamel Riahi

This paper is devoted to the numerical analysis of a control constrained distributed optimal control problem subject to a time fractional diffusion equation with non-smooth initial data. The solutions of state and co-state are decomposed…

Numerical Analysis · Mathematics 2020-10-06 Tao Wang , Binjie Li , Xiaoping Xie

We present new Dirichlet-Neumann and Neumann-Dirichlet algorithms with a time domain decomposition applied to unconstrained parabolic optimal control problems. After a spatial semi-discretization, we use the Lagrange multiplier approach to…

Numerical Analysis · Mathematics 2023-08-25 Martin Jakob Gander , Liu-Di Lu

The article discusses the gradient discretisation method (GDM) for distributed optimal control problems governed by diffusion equation with pure Neumann boundary condition. Using the GDM framework enables to develop an analysis that…

Numerical Analysis · Mathematics 2018-10-09 Jerome Droniou , Neela Nataraj , Devika Shylaja

In this contribution we propose reduced order methods to fast and reliably solve parametrized optimal control problems governed by time dependent nonlinear partial differential equations. Our goal is to provide a tool to deal with the time…

Numerical Analysis · Mathematics 2023-08-08 Francesco Ballarin , Gianluigi Rozza , Maria Strazzullo

In this paper, an efficient parallel splitting method is proposed for the optimal control problem with parabolic equation constraints. The linear finite element is used to approximate the state variable and the control variable in spatial…

Optimization and Control · Mathematics 2023-02-21 Haiming Song , Jiachuan Zhang , Yongle Hao

In this paper we study the conditioning of optimal control problems constrained by linear parabolic equations with Neumann boundary conditions. While we concentrate on a given end-time target function the results hold also when the target…

Numerical Analysis · Mathematics 2025-03-24 Luise Blank

This paper focuses on optimal control problem for a class of discrete-time nonlinear systems. In practical applications, computation time is a crucial consideration when solving nonlinear optimal control problems, especially under real-time…

Optimization and Control · Mathematics 2025-04-01 Chuanzhi Lv , Xunmin Yin , Hongdan Li , Huanshui Zhang

We consider time discretization methods for abstract parabolic problems with inhomogeneous linear constraints. Prototype examples that fit into the general framework are the heat equation with inhomogeneous (time dependent) Dirichlet…

Numerical Analysis · Mathematics 2018-06-14 Igor Voulis , Arnold Reusken

The phase-field method has emerged as a powerful tool for simulating fracture mechanics, yet it presents significant numerical challenges, particularly regarding the enforcement of physical constraints such as irreversibility and…

Numerical Analysis · Mathematics 2026-04-30 Miguel Castillón , Biswajit Khara , Jørgen S. Dokken , Thomas M. Surowiec , Brendan Keith , Yuri Bazilevs

In this work, we propose to efficiently solve time dependent parametrized optimal control problems governed by parabolic partial differential equations through the certified reduced basis method. In particular, we will exploit an error…

Numerical Analysis · Mathematics 2021-03-10 Maria Strazzullo , Francesco Ballarin , Gianluigi Rozza

In this work we recast parametrized time dependent optimal control problems governed by partial differential equations in a saddle point formulation and we propose reduced order methods as an effective strategy to solve them. Indeed, on one…

Numerical Analysis · Mathematics 2023-08-08 Maria Strazzullo , Francesco Ballarin , Gianluigi Rozza

A linearized numerical scheme is proposed to solve the nonlinear time fractional parabolic problems with time delay. The scheme is based on the standard Galerkin finite element method in the spatial direction, the fractional Crank-Nicolson…

Numerical Analysis · Mathematics 2021-09-10 Lili Li , Mianfu She , Yuanling Niu

We study the numerical approximation of linear-quadratic optimal control problems subject to the fractional Laplace equation with its spectral definition. We compute an approximation of the state equation using a discretization of the…

Numerical Analysis · Mathematics 2018-09-28 Stefan Dohr , Christian Kahle , Sergejs Rogovs , Piotr Swierczynski

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

These notes present preliminary results regarding two different approximations of linear infinite-horizon optimal control problems arising in model predictive control. Input and state trajectories are parametrized with basis functions and a…

Optimization and Control · Mathematics 2016-09-04 Michael Muehlebach , Raffaello D'Andrea

We propose a direct numerical method for the solution of an optimal control problem governed by a two-side space-fractional diffusion equation. The presented method contains two main steps. In the first step, the space variable is…

Optimization and Control · Mathematics 2019-01-29 Mushtaq Salh Ali , Mostafa Shamsi , Hassan Khosravian-Arab , Delfim F. M. Torres , Farid Bozorgnia

We consider a linear-quadratic pde constrained optimal control problem on an evolving surface with pointwise state constraints. We reformulate the optimization problem on a fixed surface and approximate the reformulated problem by a…

Optimization and Control · Mathematics 2016-04-27 Michael Hinze , Heiko Kröner