Parallel Lagrange-Newton-Krylov-Schur Methods for PDE-Constrained Optimization. Part I: The Krylov-Schur Solver

By George Biros, Omar Ghattas. SIAM Journal on Scientific Computing, 2005

300 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/8b6657a8c2c07ebdfcb492878310c0b33192cff4

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

Review and Unification of Methods for Computing Derivatives of Multidisciplinary Computational Models (2013, methodology): “Examples of such algorithms include Newton–Krylov methods applied to the solution of the Euler equations [34] and coupled aerostructural equations [11, 12, 42, 44].”
Algorithms for PDE‐constrained optimization (2010, methodology): “[Biros and Ghattas(2005)] G. Biros and O. Ghattas.”
Domain decomposition methods for advection dominated linear-quadratic elliptic optimal control problems (2005, methodology): “We present an optimization-level domain decomposition (DD) preconditioner for the solution of advection dominated elliptic linear–quadratic optimal control problems, which arise in many science and engineering applications.”
A Newton-CG method for large-scale three-dimensional elastic full-waveform seismic inversion (2008, methodology): “In one such realization of this full space approach, the Lagrange–Newton–Krylov–Schur (LNKS) method [14, 15], the optimum has been found in as little as five times the cost of solving the forward PDE problem, for problems with as many as a million state variables.”
Recent computational developments in Krylov subspace methods for linear systems (2007, background): “2; for KKT systems or saddle point problems [33], [100]; or for integral operators [203]; considerations for parallel computers [82], [104], [178]; methods for singular matrices [134], [198], [262]; or for regularization of ill-posed problems [58], [179]; multiple right-hand side and block methods [”
ANODE: Unconditionally Accurate Memory-Efficient Gradients for Neural ODEs (2019, methodology): “Adjoint Methods: Adjoint based methods have been widely used to solve problems ranging from classical optimal control problems [22] and large scale inverse problems [2, 3], to climate simulation [6, 21].”
Neurobiology of Aging: Contents (2005, unknown): “See also Arbenz et al. (2001), Biros and Ghattas (2005a, 2005b) and Haber and Ascher (2001) for similar approaches in different application contexts.”