An Inertial Proximal Method for Maximal Monotone Operators via Discretization of a Nonlinear Oscillator with Damping

By Felipe Alvarez, Hédy Attouch. 2001

793 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/cc6f5d55c8c59959bb23f6adbc7c0a38c7c0e070

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Citations in the corpus

Fast convergence of inertial dynamics and algorithms with asymptotic vanishing viscosity (2018, methodology): “For dynamics with inertial features, see [2], [3], [4], [9].”
iPiano: Inertial Proximal Algorithm for Nonconvex Optimization (2014, methodology): “In [2, 1], the Heavy-ball method has been extended to maximal monotone operators, e.”
On the Convergence of the Iterates of the “Fast Iterative Shrinkage/Thresholding Algorithm” (2015, methodology): “The proof of the theorem follows the ideas of Pock and Lorenz, in the proof of Theorem 1 in [11]—see also [12].”
An inertial forward–backward splitting method for solving inclusion problems in Hilbert spaces (2018, neutral): “For first-order gradient systems and subdifferential inclusions, see also [1,2,4].”
Inertial Douglas-Rachford splitting for monotone inclusion problems (2014, methodology): “rs in the update rules of the iterates. In this paper we introduce and investigate the convergence properties of an inertial Douglas-Rachford splitting algorithm. Inertial proximal methods go back to [1,3], where it has been noticed that the discretization of a dierential system of second-order in t”
On the convergence of the iterates of "FISTA" (2015, methodology): “The proof of the theorem follows the ideas of Pock and Lorenz, in the proof of Theorem 1 in [9]—see also [1].”
Some developments in general variational inequalities (2004, methodology): “The proof for the case a > 0 is exactly the same as in Alvarez and Attouch [6].”
On the ergodic convergence rates of a first-order primal–dual algorithm (2016, methodology): “Next, we consider an inertial version of the primal-dual algorithm, who has recently been considered in [19] as an extension of the inertial proximal point algorithm of Alvarez and Attouch [1].”
A strong convergence result involving an inertial forward–backward algorithm for monotone inclusions (2017, methodology): “In [4], Alvarez and Attouch translated the idea of the heavy ball method in [51,52] to the setting of a general maximal monotone operator using the framework of the proximal point algorithm.”
Weak Convergence of a Relaxed and Inertial Hybrid Projection-Proximal Point Algorithm for Maximal Monotone Operators in Hilbert Space (2003, methodology): “The following elementary result is a useful tool for proving convergence for this type of recursive finite difference inequality (see [1, 2]).”
New Trends in General Variational Inequalities (2020, background): “See [6, 7, 8, 9, 10, 17, 18, 24, 36, 37, 39, 42, 43, 44, 49, 55, 63, 68, 71, 79, 82, 83, 90, 92, 95, 100, 101, 102, 103, 104, 106, 107, 110, 111, 112, 113, 114, 116, 117, 119, 120, 133, 134, 135, 137, 138, 143, 144, 145, 146, 150, 152, 153, 160] and the references therein.”