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An abstract convergence theorem for a class of generalized descent methods that explicitly models relative errors is proved.
Une propriété topologique des sous-ensembles analytiques réels
S. Łojasiewicz · 1963
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Some methods of speeding up the convergence of iteration methods
B. T. Polyak · 1964
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The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming
L. M. Bregman · 1967
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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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Approximation of functionals depending on jumps by elliptic functionals via
L. Ambrosio and V. Tortorelli · 1990
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Asymptotic properties of the Fenchel dual functional and applications to decomposition problems
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Sur la géométrie semi- et sous- analytique
S. Łojasiewicz · 1993
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Heavy-ball method in nonconvex optimization problems
S. Zavriev and F. Kostyuk · 1993
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w f w_{f} -stratification of subanalytic functions and the Łojasiewicz inequality
K. Kurdyka and A. Parusiński · 1994
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Model completeness results for expansions of the ordered field of real numbers by restricted Pfaffian functions and the exponential function
A. J. Wilkie · 1996
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Tame topology and o \mathrm{o} -minimal structures
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Convergence of solutions of second-order gradient-like systems with analytic nonlinearities
A. Haraux and M. Jendoubi · 1998
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On gradients of functions definable in o-minimal structures
K. Kurdyka · 1998
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Variational Analysis
R. T. Rockafellar and R. J.-B. Wets · 1998
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Globally convergent block-coordinate techniques for unconstrained optimization
L. Grippof and M. Sciandrone · 1999
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A hybrid approximate extragradient–proximal point algorithm using the enlargement of a maximal monotone operator
M. Solodov and B. Svaiter · 1999
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A hybrid projection-proximal point algorithm
M. Solodov and B. Svaiter · 1999
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Convergence in gradient-like systems which are asymptotically autonomous and analytic
S.-Z. Huang and P. Takáč · 2001
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A unified framework for some inexact proximal point algorithms
M. Solodov and B. Svaiter · 2001
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Convergence to steady states in asymptotically autonomous semilinear evolution equations
R. Chill and M. Jendoubi · 2003
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Inexact variants of the proximal point algorithm without monotonicity
A. Iusem, T. Pennanen, and B. Svaiter · 2003
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A tutorial on MM algorithms
D. R. Hunter and K. Lange · 2004
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Introductory lectures on convex optimization: A basic course
Y. Nesterov · 2004
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Convergence of the iterates of descent methods for analytic cost functions
P. Absil, R. Mahony, and B. Andrews · 2005
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Towards PDE-based image compression
I. Galic, J. Weickert, M. Welk, A. Bruhn, A. Belyaev, and H.-P. Seidel · 2005
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The Łojasiewicz inequality for nonsmooth subanalytic functions with applications to subgradient dynamical systems
J. Bolte, A. Daniilidis, and A. Lewis · 2006
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Variable metric forward–backward splitting with applications to monotone inclusions in duality
P. Combettes and B. V. u · 2014
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Splitting methods with variable metric for Kurdyka–Łojasiewicz functions and general convergence rates
P. Frankel, G. Garrigos, and J. Peypouquet · 2014
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iPiano: Inertial proximal algorithm for non-convex optimization
P. Ochs, Y. Chen, T. Brox, and T. Pock · 2014
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An inertial Tseng’s type proximal algorithm for nonsmooth and nonconvex optimization problems
R. I. Bot and E. R. Csetnek · 2015
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An inertial forward–backward algorithm for the minimization of the sum of two nonconvex functions
R. I. Bot, E. R. Csetnek, and S. László · 2015
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Clarke subgradients of stratifiable functions
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Pointwise convergence of gradient-like systems
C. Lageman · 2007
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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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M. Mainberger and J. Weickert · 2009
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Global convergence of splitting methods for nonconvex composite optimization
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Peaceman–Rachford splitting for a class of nonconvex optimization problems
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Long term motion analysis for object level grouping and nonsmooth optimization methods
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Majorization-minimization procedures and convergence of SQP methods for semi-algebraic and tame programs
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Douglas–Rachford splitting for nonconvex optimization with application to nonconvex feasibility problems
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