On the Convergence of the Iterates of the “Fast Iterative Shrinkage/Thresholding Algorithm”

By Antonin Chambolle, Charles Dossal. Journal of Optimization Theory and Applications, 2015

442 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Mechanics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/b2e847be6467642fc7aa0af3e35ad2753dffa35f

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Citations in the corpus

An introduction to continuous optimization for imaging (2016, methodology): “Variants of this choice which ensure, in addition, convergence of the iterates (xk)k to a solution, are discussed in Chambolle and Dossal (2015).”
Calculus of the Exponent of Kurdyka–Łojasiewicz Inequality and Its Applications to Linear Convergence of First-Order Methods (2016, methodology): “hod of multipliers, etc. Due to the excellent performance and wide applicability of the rst-order methods, their convergence behaviors have been extensively studied in recent years; see, for example, [1, 2, 3, 7, 16, 18, 23, 34] and references therein. Analyzing the convergence rate of the rst-order”
Stochastic Approximations and Perturbations in Forward-Backward Splitting for Monotone Operators (2015, background): “Recent theoretical advances on deterministic versions of this algorithm can be found in [6, 11, 20, 22].”
Rate of convergence of the Nesterov accelerated gradient method in the subcritical case α ≤ 3 (2017, unknown): “D GRADIENT 19 4.6. Convergenceofiterates. Thecriticalcaseα = 3. In the case α > 3, as a major result, the weak convergence of the sequences generated by (IFB)α was obtained by Chambolle and Dossal [17], and completed by Attouch-ChbaniPeypouquet-Redont [5]. The case α = 3 corresponds to the accele”
A self adaptive inertial subgradient extragradient algorithm for variational inequality and common fixed point of multivalued mappings in Hilbert spaces (2019, background): “Recently, several of researchers have constructed some fast iterative algorithms by using inertial extrapolation which includes inertial proximal methods [31, 32], inertial forward-backward methods [33], inertial split equilibriummethods [34], inertial proximal ADMM [35] and the fast iterative shrin”