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We investigate the numerical approximation of an elliptic optimal control problem which involves a nonconvex local regularization of the $L^q$-quasinorm penalization (with $q\in(0,1)$) in the cost function. Our approach is based on the…

Optimization and Control · Mathematics 2022-09-26 Pedro Merino , Alexander Nenjer

Optimal Control Problems consist on the optimisation of an objective functional subjected to a set of Ordinary Differential Equations. In this work, we consider the effects on the stability of the numerical solution when this optimisation…

Optimization and Control · Mathematics 2024-01-09 Ashutosh Bijalwan , Jose J Muñoz

We study an optimal control problem for the stochastic wave equation driven by affine multiplicative noise, formulated as a stochastic linear-quadratic (SLQ) problem. By applying a stochastic Pontryagin's maximum principle, we characterize…

Optimization and Control · Mathematics 2025-10-30 Abhishek Chaudhary

We design a primal-dual stabilized finite element method for the numerical approximation of a data assimilation problem subject to the acoustic wave equation. For the forward problem, piecewise affine, continuous, finite element functions…

Numerical Analysis · Mathematics 2023-05-10 Erik Burman , Ali Feizmohammadi , Lauri Oksanen

A family of implicit-in-time mixed finite element schemes is presented for the numerical approximation of the acoustic wave equation. The mixed space discretization is based on the displacement form of the wave equation and the…

Numerical Analysis · Mathematics 2015-04-17 Samir Karaa

A numerical method is proposed for a class of stochastic control problems including singular behavior. This method solves an infinite-dimensional linear program equivalent to the stochastic control problem using a finite element type…

Probability · Mathematics 2018-06-11 Martin G. Vieten , Richard H. Stockbridge

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

A general backward stochastic linear-quadratic optimal control problem is studied, in which both the state equation and the cost functional contain the nonhomogeneous terms. The main feature of the problem is that the weighting matrices in…

Optimization and Control · Mathematics 2022-03-01 Jingrui Sun , Jiaqiang Wen , Jie Xiong

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

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 consider linear quadratic optimal control with mean-field type for discrete-time stochastic systems with state and control dependent noise. An optimal control problem is studied for a linear mean-field stochastic…

Optimization and Control · Mathematics 2022-10-06 Arzu Ahmadova , Nazim I. Mahmudov

We study the optimal value function for control problems on Banach spaces that involve both continuous and discrete control decisions. For problems involving semilinear dynamics subject to mixed control inequality constraints, one can show…

Optimization and Control · Mathematics 2017-01-11 Martin Gugat , Falk M. Hante

In this paper, error estimates are presented for a certain class of optimal control problems with elliptic PDE-constraints. It is assumed that in the cost functional the state is measured in terms of the energy norm generated by the state…

Numerical Analysis · Mathematics 2014-10-31 Olli Mali

We study the minimization of the expected costs under stochastic constraint at the terminal time. The first and the main result says that for a power type of costs, the value function is the minimal positive solution of a second order…

Probability · Mathematics 2020-01-28 Yan Dolinsky , Benjamin Gottesman , Ori Gurel-Gurevich

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

In this paper we consider the convergence analysis of adaptive finite element method for elliptic optimal control problems with pointwise control constraints. We use variational discretization concept to discretize the control variable and…

Numerical Analysis · Mathematics 2016-08-31 Wei Gong , Ningning Yan

We examine the minimization of a quadratic cost functional composed of the output and the final state of abstract infinite-dimensional evolution equations in view of existence of solutions and optimality conditions. While the initial value…

Optimization and Control · Mathematics 2024-12-20 Timo Reis , Manuel Schaller

We consider a distributed optimal control problem subject to a parabolic evolution equation as constraint. The control will be considered in the energy norm of the anisotropic Sobolev space $[H_{0;,0}^{1,1/2}(Q)]^\ast$, such that the state…

Numerical Analysis · Mathematics 2025-02-14 Richard Löscher , Michael Reichelt , Olaf Steinbach

We consider a stabilized finite element method based on a spacetime formulation, where the equations are solved on a global (unstructured) spacetime mesh. A unique continuation problem for the wave equation is considered, where data is…

Numerical Analysis · Mathematics 2023-05-10 Erik Burman , Ali Feizmohammadi , Arnaud Munch , Lauri Oksanen

Stability and optimal convergence analysis of a non-uniform implicit-explicit L1 finite element method (IMEX-L1-FEM) is studied for a class of time-fractional linear partial differential/integro-differential equations with non-self-adjoint…

Numerical Analysis · Mathematics 2024-03-19 Aditi Tomar , Lok Pati Tripathi , Amiya K. Pani