Continuation and path following

By Eugene L. Allgower, Kurt Georg. 1993

Subfields: Mathematical Optimization, Numerical Methods & Scientific Computing

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Citations in the corpus

Minding the Gaps for Block Frank-Wolfe Optimization of Structured SVMs (2016, background): “Exact path following algorithms suffer from numerical instabilities as they repeatedly invert a potentially badly-conditioned matrix (Allgower & Georg, 1993).”
Jacobian-free Newton-Krylov methods: a survey of approaches and applications (2004, background): “A nice survey paper on continuation methods is [1].”
Interior Methods for Nonlinear Optimization (2002, unknown): “, [1, 2]) has been recognized since the early days of modern interior methods (see, e.”
Deflation Techniques for Finding Distinct Solutions of Nonlinear Partial Differential Equations (2014, unknown): “We emphasise that more sophisticated continuation algorithms such as pseudo-arclength continuation [40, 3] could naturally be combined with deﬂation.”
An Inexact Cayley Transform Method For Inverse Eigenvalue Problems (2004, methodology): “In these continuous methods, our inexact method can be used as the corrector step where a valid starting point is provided by the globalization strategy, see for examples [3] and [37, pp.”
What is numerical algebraic geometry (2017, background): “Allgower and Georg’s book [4] and articles [2, 3] provide surveys of this theory with the important case of polynomial systems placed in the perspective of much more general systems.”
Introduction to numerical algebraic geometry (2005, methodology): “Continuation or path-following methods are standard numerical techniques ([1, 2, 3], [57], [107, 108]) to trace the solution paths defined by the homotopy using predictor-corrector methods.”
An Interior-Point Method for Large-Scale l1-Regularized Logistic Regression (2007, methodology): “These methods are related to numerical continuation techniques for following piecewise smooth curves, which have been well studied in the optimization literature [1].”