Numerical continuation methods - an introduction

By Eugene L. Allgower, Kurt Georg. 1990

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Citations in the corpus

Rigorous Numerics for the Cahn-Hilliard Equation on the Unit Square (2008, background): “Observe that in case Ω = [0, 1] the definitions φ0,0 = 1 and φi,j(x, y) = cos(iπx) cos(jπy), for all (i, j) ∈ N \ {(0, 0)} (7) furnish a complete orthogonal basis for the Hilbert space L(Ω).”
From Baby Steps to Leapfrog: How “Less is More” in Unsupervised Dependency Parsing (2010, background): “They conjectured that a well-chosen sequence of training criteria — different sets of weights on the examples — could act as a continuation method (Allgower and Georg, 1990), helping find better local optima for nonconvex objectives.”
Scheduled denoising autoencoders (2014, background): “a points to move between cluster centroids early in the optimization process. ScheDA is also conceptually related to curriculum learning [Bengio et al., 2009] and continuation methods more generally [Allgower and Georg, 1980]. However, our motivation is different. In curriculum learning, the network”
SOLVING SYSTEMS OF POLYNOMIAL EQUATIONS (2002, unknown): “Standard references include [AG90] and [Li97].”
Estimating Static Models of Strategic Interactions (2010, methodology): “Algorithms for implementing the homotopy method can be found in several papers including Watson, Billups, and Morgan (1987), Kostreva and Kinard (1991), Allgower and Georg (1980) and Watson, Sosonkina, Melville, Morgan, and Walker (1997).”
Clustering by Scale-Space Filtering (2000, methodology): “This means that cluster centers form simple curves in the scale space which can be computed through the path that follows the solutions of the equation 5xP x; 0 by the continuational method [32].”
C-MIL: Continuation Multiple Instance Learning for Weakly Supervised Object Detection (2019, methodology): “3 and discover better solutions [3, 31], Fig.”
On Graduated Optimization for Stochastic Non-Convex Problems (2015, background): “Concepts of the same nature appeared in the optimization literature Wu (1996), and in the field of numerical analysis Allgower and Georg (1990).”
Rigid-Body Dynamics with Friction and Impact (2000, methodology): “These methods can be made global by using continuation methods (see, for example, [1, 140] for overviews of practical homotopy/continuation methods and [101] for a theoretical analysis of the basis for using continuation methods for frictional contact problems).”
Self-Paced Learning for Latent Variable Models (2010, unknown): “[3] noted that curriculum learning can be seen as a type of continuation method [1].”
Constructive Methods for Initialization and Handling Mixed State-Input Constraints in Optimal Control (2008, background): “They appear to be well suited for aerospace trajectory optimization problems and are currently used, along with ideas fromnonlinear geometric control, on various ascent and reentry problems.”