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This paper studies the Craig variant of the Golub-Kahan bidiagonalization algorithm as an iterative solver for linear systems with saddle point structure. Such symmetric indefinite systems in 2x2 block form arise in many applications, but…

Computational Engineering, Finance, and Science · Computer Science 2018-08-24 Mario Arioli , Carola Kruse , Ulrich Ruede , Nicolas Tardieu

In this paper, we present a method that enables to solve in parallel the Euler-Lagrange system associated with the optimal control of a parabolic equation. Our approach is based on an iterative update of a sequence of intermediate targets…

Optimization and Control · Mathematics 2011-10-19 Yvon Maday , Julien Salomon , Kamel Riahi

This paper deals with balanced domain decomposition by constraints (BDDC) method for solving large-scale linear systems of algebraic equations arising from the space-time finite element discretization of parabolic initial-boundary value…

Numerical Analysis · Mathematics 2018-10-30 Ulrich Langer , Huidong Yang

In this paper, we investigate an optimal control problem governed by parabolic equations with measure-valued controls over time. We establish the well-posedness of the optimal control problem and derive the first-order optimality condition…

Optimization and Control · Mathematics 2024-04-04 Wei Gong , Dongdong Liang

This paper is concerned with the weak solvability of fully nonlinear parabolic variational inequalities with time dependent convex constraints. As possible approaches to such problems, there are for instance the time-discretization method…

Functional Analysis · Mathematics 2017-06-21 Maria Gokieli , Nobuyuki Kenmochi , Marek Niezgódka

In the present paper, we focus on the vector optimization problems with inequality constraints, where objective functions and constrained functions are Fr\'echet differentiable, and whose gradient mapping is locally Lipschitz on an open…

Optimization and Control · Mathematics 2017-05-08 Nguyen Quang Huy , Do Sang Kim , Nguyen Van Tuyen

We propose an efficient numerical algorithm for the solution of diffeomorphic image registration problems. We use a variational formulation constrained by a partial differential equation (PDE), where the constraints are a scalar transport…

Optimization and Control · Mathematics 2018-03-02 Andreas Mang , George Biros

We consider discontinuous Galerkin methods for an elliptic distributed optimal control problem constrained by a convection-dominated problem. We prove global optimal convergence rates using an inf-sup condition, with the diffusion parameter…

Numerical Analysis · Mathematics 2024-06-14 Sijing Liu , Valeria Simoncini

This paper proposes a new method for differentiating through optimal trajectories arising from non-convex, constrained discrete-time optimal control (COC) problems using the implicit function theorem (IFT). Previous works solve a…

Machine Learning · Computer Science 2023-10-25 Ming Xu , Timothy Molloy , Stephen Gould

The Allen-Cahn equation is a fundamental model for phase transitions, offering critical insights into the dynamics of interface evolution in various physical systems. This paper investigates the stability and robustness of frequently…

Numerical Analysis · Mathematics 2025-04-11 Wenrui Hao , Sun Lee , Xiaofeng Xu , Zhiliang Xu

The conic bundle implementation of the spectral bundle method for large scale semidefinite programming solves in each iteration a semidefinite quadratic subproblem by an interior point approach. For larger cutting model sizes the limiting…

Optimization and Control · Mathematics 2023-08-25 Christoph Helmberg

The result after $N$ steps of an implicit Runge-Kutta time discretization of an inhomogeneous linear parabolic differential equation is computed, up to accuracy $\epsilon$, by solving only $$O\Big(\log N \log \frac1\epsilon \Big) $$ linear…

Numerical Analysis · Mathematics 2011-11-10 María López-Fernández , Christian Lubich , Cesar Palencia , Achim Schädle

Monitoring the integrity of elastic structures using ultrasonic waves requires the efficient identification of material parameters from measured surface displacements. The displacement field is governed by Cauchy's equation of motion, i.e.,…

Numerical Analysis · Mathematics 2026-05-20 Benedikt Klein , Mario Ohlberger , Thomas Schuster

We present and analyze a stable space-time multi-patch discontinuous Galerkin Isogeometric Analysis (dG-IgA) scheme for the numerical solution of parabolic evolution equations in moving space-time computational domains. Following…

Numerical Analysis · Mathematics 2017-07-27 Stephen Edward Moore

We consider a general linear parabolic problem with extended time boundary conditions (including initial value problems and periodic ones), and approximate it by the implicit Euler scheme in time and the Gradient Discretisation method in…

Numerical Analysis · Mathematics 2023-08-22 J Droniou , R Eymard , T Gallouët , C Guichard , R Herbin

Preconditioned iterative methods for numerical solution of large matrix eigenvalue problems are increasingly gaining importance in various application areas, ranging from material sciences to data mining. Some of them, e.g., those using…

Numerical Analysis · Mathematics 2017-05-12 Merico E. Argentati , Andrew V. Knyazev , Klaus Neymeyr , Evgueni E. Ovtchinnikov , Ming Zhou

Accurate determination of particle track reconstruction parameters will be a major challenge for the High Luminosity Large Hadron Collider (HL-LHC) experiments. The expected increase in the number of simultaneous collisions at the HL-LHC…

The Legendre spectral Galerkin method of self-adjoint second order elliptic equations usually results in a linear system with a dense and ill-conditioned coefficient matrix. In this paper, the linear system is solved by a preconditioned…

Numerical Analysis · Mathematics 2020-04-30 Xuhao Diao , Jun Hu , Suna Ma

Some necessary and sufficient optimality conditions for inequality constrained problems with continuously differentiable data were obtained in the papers [I. Ginchev and V.I. Ivanov, Second-order optimality conditions for problems with…

Optimization and Control · Mathematics 2018-05-24 Vsevolod I. Ivanov

Implicit Runge--Kutta (IRK) methods are highly effective for solving stiff ordinary differential equations (ODEs) but can be computationally expensive for large-scale problems due to the need of solving coupled algebraic equations at each…

Numerical Analysis · Mathematics 2025-09-18 Fabio Durastante , Mariarosa Mazza