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We investigate symmetry reduction of optimal control problems for left-invariant control systems on Lie groups, with partial symmetry breaking cost functions. Our approach emphasizes the role of variational principles and considers a…

Optimization and Control · Mathematics 2017-01-25 Anthony Bloch , Leonardo Colombo , Rohit Gupta , Tomoki Ohsawa

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

This work addresses an optimal control problem for a semilinear elliptic equation in two-dimensional space, characterized by an exponential nonlinearity and a singular source term. The source is modeled as a finite linear combination of…

Optimization and Control · Mathematics 2025-05-28 Vu Huu Nhu

We consider a risk-averse optimal control problem governed by an elliptic variational inequality (VI) subject to random inputs. By deriving KKT-type optimality conditions for a penalised and smoothed problem and studying convergence of the…

Optimization and Control · Mathematics 2025-05-26 Amal Alphonse , Caroline Geiersbach , Michael Hintermüller , Thomas M. Surowiec

In this paper we study a discrete variational optimal control problem for the rigid body. The cost to be minimized is the external torque applied to move the rigid body from an initial condition to a pre-specified terminal condition.…

Optimization and Control · Mathematics 2007-12-31 Anthony M. Bloch , Islam I. Hussein , Melvin Leok , Amit K. Sanyal

Motivated by the fact that both the classical and quantum description of nature rest on causality and a variational principle, we develop a novel and highly versatile discretization prescription for classical initial value problems (IVPs).…

Numerical Analysis · Mathematics 2023-02-15 Alexander Rothkopf , Jan Nordström

In this article, we develop a posteriori error analysis of a nonconforming finite element method for a linear quadratic elliptic distributed optimal control problem with two different set of constraints, namely (i) integral state constraint…

Optimization and Control · Mathematics 2021-08-09 Kamana Porwal , Pratibha Shakya

We study the discretization of an elliptic partial differential equation, posed on a two- or three-dimensional domain with smooth boundary, endowed with a generalized Robin boundary condition which involves the Laplace-Beltrami operator on…

Numerical Analysis · Mathematics 2020-09-24 Dominik Edelmann

A finite element analysis of a Dirichlet boundary control problem governed by the linear parabolic equation is presented in this article. The Dirichlet control is considered in a closed and convex subset of the energy space $H^1(\Omega…

Numerical Analysis · Mathematics 2021-11-04 Thirupathi Gudi , Gouranga Mallik , Ramesh Ch. Sau

In this work, we study a boundary control problem for the evolutionary Navier-Stokes equations, under mixed boundary conditions, in two dimensions. The cost functional here considered is of quadratic type, depending on both state and…

Optimization and Control · Mathematics 2024-10-02 Telma Guerra , Irene Marín-Gayte , Jorge Tiago

The present paper represents a continuation of our previous one. There, a continuous dependence result for the solution of an elliptic variational-hemivariational inequality was obtained and then used to prove the existence of optimal pairs…

Analysis of PDEs · Mathematics 2019-12-25 Yi-bin Xiao , Mircea Sofonea

We propose and analyze a monotone finite element method for an elliptic distributed optimal control problem constrained by a convection-diffusion-reaction equation in the convection-dominated regime. The method is based on the edge-averaged…

Numerical Analysis · Mathematics 2025-11-04 SeongHee Jeong , Seulip Lee , Sijing Liu

We introduce a variational algorithm to estimate the likelihood of a rare event within a nonequilibrium molecular dynamics simulation through the evaluation of an optimal control force. Optimization of a control force within a chosen basis…

Statistical Mechanics · Physics 2021-01-14 Avishek Das , David T. Limmer

We consider a linear-quadratic optimization problem with pointwise bounds on the state for which the constraint is given by the Laplace-Beltrami equation (to have uniqueness we add an lower order term) on a two-dimensional surface . By…

Optimization and Control · Mathematics 2016-06-10 Ahmad Ahmad Ali , Michael Hinze , Heiko Kröner

In this paper, an abstract framework for the error analysis of discontinuous finite element method is developed for the distributed and Neumann boundary control problems governed by the stationary Stokes equation with control constraints.…

Numerical Analysis · Mathematics 2021-11-01 Asha K Dond , Thirupathi Gudi , Ramesh Ch. Sau

The present paper studies finite element discretizations of second-order elliptic boundary value problems with homogeneous right-hand side and inhomogeneous boundary conditions. We establish discrete spatial decay estimates on element…

Numerical Analysis · Mathematics 2026-04-27 Tim Buchholz , Julian Dörner

In this paper, we deal with an elliptic problem with the Dirichlet boundary condition. We operate in Sobolev spaces and the main analytic tool we use is the Lax-Milgram lemma. First, we present the variational approach of the problem which…

Analysis of PDEs · Mathematics 2025-02-12 Eriselda Goga , Besiana Hamzallari

The paper studies a class of quadratic optimal control problems for partially observable linear dynamical systems. In contrast to the full information case, the control is required to be adapted to the filtration generated by the…

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

This paper studies formulations of second-order elliptic partial differential equations in nondivergence form on convex domains as equivalent variational problems. The first formulation is that of Smears \& S\"uli [SIAM J.\ Numer.\ Anal.\…

Numerical Analysis · Mathematics 2017-01-17 Dietmar Gallistl

We consider control constrained optimal control problems governed by parameterized stationary Maxwell's system with the Gauss's law. The parameters enter through dielectric, magnetic permeability, and charge density. Moreover, the parameter…

Optimization and Control · Mathematics 2020-04-20 Harbir Antil , Tran Nhan Tam Quyen