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We study a control-constrained optimal control problem governed by a semilinear elliptic equation. The control acts in a bilinear way on the boundary, and can be interpreted as a heat transfer coefficient. A detailed study of the state…

Optimization and Control · Mathematics 2024-03-06 Eduardo Casas , Konstantinos Chrysafinos , Mariano Mateos

The problem of quantum state preparation is one of the main challenges in achieving the quantum advantage. Furthermore, classically, for multi-level problems, our ability to solve the corresponding quantum optimal control problems is rather…

In this paper, we investigate optimal boundary control problems for Cahn-Hilliard variational inequalities with a dynamic boundary condition involving double obstacle potentials and the Laplace-Beltrami operator. The cost functional is of…

Analysis of PDEs · Mathematics 2014-09-29 Pierluigi Colli , M. Hassan Farshbaf-Shaker , Gianni Gilardi , Jürgen Sprekels

We consider a saddle point formulation for a sixth order partial differential equation and its finite element approximation, for two sets of boundary conditions. We follow the Ciarlet-Raviart formulation for the biharmonic problem to…

Numerical Analysis · Mathematics 2017-11-17 Jérôme Droniou , Muhammad Ilyas , Bishnu Lamichhane , Glen E. Wheeler

An inherent regularization strategy and block Schur complement preconditioning are studied for linear poroelasticity problems discretized using the lowest-order weak Galerkin FEM in space and the implicit Euler scheme in time. At each time…

Numerical Analysis · Mathematics 2025-07-31 Weizhang Huang , Zhuoran Wang

This paper is concerned with robust preconditioning of wave equations constrained linear inverse problems from boundary observation data. The main result of this paper is a concept for regularization parameter robust preconditioning.…

Analysis of PDEs · Mathematics 2020-01-08 Alexander Beigl , Otmar Scherzer , Jarle Sogn , Walter Zulehner

We consider convex-concave saddle point problems with a separable structure and non-strongly convex functions. We propose an efficient stochastic block coordinate descent method using adaptive primal-dual updates, which enables flexible…

Machine Learning · Statistics 2015-11-24 Zhanxing Zhu , Amos J. Storkey

Recently, in (M. Masoudi, D.K. Salkuyeh, An extension of positive-definite and skew-Hermitian splitting method for preconditioning of generalized saddle point problems, Computers \& Mathematics with Application,…

Numerical Analysis · Mathematics 2021-09-13 Mohsen Masoudi , Davod Khojasteh Salkuyeh

This paper studies the primal-dual convergence and iteration-complexity of proximal bundle methods for solving nonsmooth problems with convex structures. More specifically, we develop a family of primal-dual proximal bundle methods for…

Optimization and Control · Mathematics 2025-09-26 Jiaming Liang

We propose a novel preconditioned inexact primal-dual interior point method for constrained convex quadratic programming problems. The algorithm we describe invokes the preconditioned conjugate gradient method on a new reduced Schur…

Numerical Analysis · Mathematics 2021-12-28 Samah Karim , Edgar Solomonik

In this paper we address the numerical solution of the quadratic optimal transport problem in its dynamical form, the so-called Benamou-Brenier formulation. When solved using interior point methods, the main computational bottleneck is the…

Numerical Analysis · Mathematics 2024-01-22 Enrico Facca , Gabriele Todeschi , Andrea Natale , Michele Benzi

The paper deals with a stochastic Galerkin approximation of elliptic Dirichlet boundary control problems with random input data. The expectation of a tracking cost functional with the deterministic constrained control is minimized. Error…

Optimization and Control · Mathematics 2025-06-16 Max Winkler , Hamdullah Yücel

This paper is concerned with a boundary control problem for the Cahn--Hilliard equation coupled with dynamic boundary conditions. In order to handle the control problem, we restrict our analysis to the case of regular potentials defined on…

Analysis of PDEs · Mathematics 2021-01-20 Pierluigi Colli , Andrea Signori

We construct multigrid methods for an elliptic distributed optimal control problem that are robust with respect to a regularization parameter. We prove the uniform convergence of the $W$-cycle algorithm and demonstrate the performance of…

Numerical Analysis · Mathematics 2018-12-03 Susanne C. Brenner , Sijing Liu , Li-yeng Sung

In this paper, an optimal control problem governed by a class of p-Laplacian elliptic equations is studied. In particular, as no monotonicity assumption is assumed on the nonlinear term, the state equation may admit several solutions for…

Optimization and Control · Mathematics 2019-08-28 Hongwei Lou , Shu Luan

In this paper we study quasilinear elliptic systems driven by variable exponent double phase operators involving fully coupled right-hand sides and nonlinear boundary conditions. The aim of our work is to establish an enclosure and…

Analysis of PDEs · Mathematics 2022-08-03 Umberto Guarnotta , Roberto Livrea , Patrick Winkert

In this paper, we consider a family of simultaneous distributed-boundary optimal control problems ($P_{\alpha}$) on the internal energy and the heat flux for a system governed by a mixed elliptic variational equality with a parameter…

Optimization and Control · Mathematics 2023-03-30 Carolina M. Bollo , Claudia M. Gariboldi , Domingo A. Tarzia

PDE-constrained optimization is a field of numerical analysis that combines the theory of PDEs, nonlinear optimization and numerical linear algebra. Optimization problems of this kind arise in many physical applications, prominently in…

Numerical Analysis · Mathematics 2017-10-18 Gennadij Heidel , Andy Wathen

The elliptic restricted three body problem has been well studied. However, the previous formulations of the problem have used a rotating coordinate system to keep the positions of the primary and secondary on the x-axis. This requires the…

Classical Physics · Physics 2021-12-15 Robert W. Easton

In this work, we investigate a neural network based solver for optimal control problems (without / with box constraint) for linear and semilinear second-order elliptic problems. It utilizes a coupled system derived from the first-order…

Optimization and Control · Mathematics 2024-05-09 Yongcheng Dai , Bangti Jin , Ramesh Sau , Zhi Zhou