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This paper deals with local criteria for the convergence to a global minimiser for gradient flow trajectories and their discretisations.
A topological property of real analytic subsets
S. Łojasiewicz · 1963
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Gradient methods for the minimisation of functionals
B. Polyak · 1963
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Régularisation d’inéquations variationnelles par approximations successives
B. Martinet · 1970
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Monotone operators and the proximal point algorithm
R. T. Rockafellar · 1976
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On Lower Semicontinuity of Integral Functionals. I
A. D. Ioffe · 1977
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Asymptotics for a class of non-linear evolution equations, with applications to geometric problems
L. Simon · 1983
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Sur la géométrie semi- et sous- analytique
S. Łojasiewicz · 1993
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The Variational Formulation of the Fokker-Planck Equation
R. Jordan, D. Kinderlehrer, and F. Otto · 1998
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On gradients of functions definable in o-minimal structures
K. Kurdyka · 1998
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Metric regularity and subdifferential calculus
A. D. Ioffe · 2000
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Gradient Flows in Metric Spaces and in the Space of Probability Measures
L. Ambrosio, N. Gigli, and G. Savaré · 2008
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On the convergence of the proximal algorithm for nonsmooth functions involving analytic features
H. Attouch and J. Bolte · 2009
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A new class of transport distances between measures
J. Dolbeault, B. Nazaret, and G. Savaré · 2009
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Proximal alternating minimization and projection methods for nonconvex problems: an approach based on the Kurdyka-Łojasiewicz inequality
H. Attouch, J. Bolte, P. Redont, and A. Soubeyran · 2010
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Characterizations of Łojasiewicz inequalities: subgradient flows, talweg, convexity
J. Bolte, A. Daniilidis, O. Ley, and L. Mazet · 2010
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Gradient flows of the entropy for finite Markov chains
J. Maas · 2011
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A gradient structure for reaction-diffusion systems and for energy-drift-diffusion systems
Kurdyka-Łojasiewicz-Simon inequality for gradient flows in metric spaces
D. Hauer and J. M. Mazón · 2019
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Spherical Hellinger–Kantorovich Gradient Flows
S. Kondratyev and D. Vorotnikov · 2019
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Overparameterized nonlinear learning: Gradient descent takes the shortest path?
S. Oymak and M. Soltanolkotabi · 2019
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Gradient flows and evolution variational inequalities in metric spaces. I: Structural properties
M. Muratori and G. Savaré · 2020
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Deep learning: a statistical viewpoint
P. L. Bartlett, A. Montanari, and A. Rakhlin · 2021
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Swarm gradient dynamics for global optimization: the density case
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A. Mielke · 2011
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Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward-backward splitting, and regularized Gauss-Seidel methods
H. Attouch, J. Bolte, and B. F. Svaiter · 2013
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Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below
L. Ambrosio, N. Gigli, and G. Savaré · 2014
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Curves of descent
D. Drusvyatskiy, A. D. Ioffe, and A. S. Lewis · 2015
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Linear convergence of gradient and proximal-gradient methods under the polyak-łojasiewicz condition
H. Karimi, J. Nutini, and M. Schmidt · 2016
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A family of functional inequalities: Łojasiewicz inequalities and displacement convex functions
A. Blanchet and J. Bolte · 2018
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Memorization and optimization in deep neural networks with minimum over-parameterization
S. Bombari, M. H. Amani, and M. Mondelli · 2022
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Gradient flow dynamics of shallow ReLU networks for square loss and orthogonal inputs
E. Boursier, L. Pillaud-Vivien, and N. Flammarion · 2022
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Convergence of gradient descent for deep neural networks
S. Chatterjee · 2022
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Polyak-Łojasiewicz inequality on the space of measures and convergence of mean-field birth-death processes
L. Liu, M. B. Majka, and Ł. Szpruch · 2023
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