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Optimization algorithms can see their local convergence rates deteriorate when the Hessian at the optimum is singular.
Une propriété topologique des sous-ensembles analytiques réels
Stanislaw Łojasiewicz · 1963
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Boris T Polyak · 1963
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The modification of Newton’s method for unconstrained optimization by bounding cubic terms
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Sur les trajectoires du gradient d’une fonction analytique
Stanislaw Łojasiewicz · 1982
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Boris T Polyak · 1987
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Perturbation theory of nonlinear programs when the set of optimal solutions is not a singleton
Alexander Shapiro · 1988
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Zhi-Quan Luo and Paul Tseng · 1993
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Nonlinear Programming
D.P. Bertsekas · 1995
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Second-order sufficiency and quadratic growth for nonisolated minima
Joseph Frédéric Bonnans and Alexander Ioffe · 1995
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Proximal smoothness and the lower-C2 property
Francis H Clarke, RJ Stern, and PR Wolenski · 1995
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U. Helmke and J.B. Moore · 1996
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On gradients of functions definable in o-minimal structures
Krzysztof Kurdyka · 1998
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Degenerate nonlinear programming with a quadratic growth condition
Mihai Anitescu · 2000
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Trust region methods
Andrew R Conn, Nicholas IM Gould, and Philippe L Toint · 2000
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Metric regularity and subdifferential calculus
Aleksandr Davidovich Ioffe · 2000
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Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality
Felix Otto and Cédric Villani · 2000
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Error bounds and superlinear convergence analysis of some Newton-type methods in optimization
Paul Tseng · 2000
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On the rate of convergence of the Levenberg–Marquardt method
Nobuo Yamashita and Masao Fukushima · 2001
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A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization
Samuel Burer and Renato DC Monteiro · 2003
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Convergence of the iterates of descent methods for analytic cost functions
P-A Absil, Robert Mahony, and Benjamin Andrews · 2005
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Local minima and convergence in low-rank semidefinite programming
Samuel Burer and Renato DC Monteiro · 2005
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On the quadratic convergence of the Levenberg–Marquardt method without nonsingularity assumption
Jin-yan Fan and Ya-xiang Yuan · 2005
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The Łojasiewicz–Simon gradient inequality in Hilbert spaces
Ralph Chill · 2006
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Cubic regularization of Newton method and its global performance
Yurii Nesterov and Boris T Polyak · 2006
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Numerical Optimization
Jorge Nocedal and Stephen J Wright · 2006
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Trust-region methods on Riemannian manifolds
P-A Absil, Christopher G Baker, and Kyle A Gallivan · 2007
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A conjecture of De Giorgi on the square distance function
Giovanni Bellettini, M Masala, and Matteo Novaga · 2007
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Optimization algorithms on matrix manifolds
P-A Absil, Robert Mahony, and Rodolphe Sepulchre · 2008
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Nonlinear error bounds for lower semicontinuous functions on metric spaces
Jean-Noël Corvellec and Viorica V Motreanu · 2008
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Proximal alternating minimization and projection methods for nonconvex problems: An approach based on the Kurdyka–Łojasiewicz inequality
Hédy Attouch, Jérôme Bolte, Patrick Redont, and Antoine Soubeyran · 2010
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Characterizations of Łojasiewicz inequalities: subgradient flows, talweg, convexity
Jérôme Bolte, Aris Daniilidis, Olivier Ley, and Laurent Mazet · 2010
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Numerical optimization methods on Riemannian manifolds
Chunhong Qi · 2011
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Optimization methods on Riemannian manifolds and their application to shape space
Wolfgang Ring and Benedikt Wirth · 2012
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Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward-backward splitting, and regularized Gauss–Seidel methods
Hédy Attouch, Jérôme Bolte, and Benar Fux Svaiter · 2013
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Second-order growth, tilt stability, and metric regularity of the subdifferential
Dmitriy Drusvyatskiy, Boris S Mordukhovich, and Tran TA Nghia · 2013
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Convergence of linesearch and trust-region methods using the Kurdyka–Łojasiewicz inequality
Dominikus Noll and Aude Rondepierre · 2013
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Gradient methods for convex minimization: better rates under weaker conditions
Hui Zhang and Wotao Yin · 2013
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Proximal alternating linearized minimization for nonconvex and nonsmooth problems
Jérôme Bolte, Shoham Sabach, and Marc Teboulle · 2014
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Strong local convergence properties of adaptive regularized methods for nonlinear least squares
S Bellavia and B Morini · 2015
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Convergence of stochastic gradient descent schemes for Łojasiewicz landscapes
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