A splitting algorithm for dual monotone inclusions involving cocoercive operators

By Bang Công Vu. 2011

623 citations recorded by the source corpus.

We consider the problem of solving dual monotone inclusions involving sums of composite parallel-sum type operators. A feature of this work is to exploit explicitly the properties of the cocoercive operators appearing in the model. Several splitting algorithms recently proposed in the literature are recovered as special cases.

Subfields: Computational Theory and Mathematics, Mathematical Physics, Statistics and Probability, Optimization & Training

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Citations in the corpus

Stochastic Gradient Descent-Ascent and Consensus Optimization for Smooth Games: Convergence Analysis under Expected Co-coercivity (2021, background): “The co-coercive condition is relatively standard in operator splitting literature [Davis and Yin, 2017, V˜u, 2013] and for variational inequalities [Zhu and Marcotte, 1996].”
Distributed Fixed Point Methods with Compressed Iterates (2019, methodology): “Vu-Condat splitting Vu condat splitting [11, 30] is an optimization algorithm to minimize a sum of three convex functions F (x) +G(x) +H(Ax) where A is a matrix.”
A New Primal–Dual Algorithm for Minimizing the Sum of Three Functions with a Linear Operator (2016, methodology): “Condat-Vu : The Condat-Vu algorithm [12,34] is a generalization of the Chambolle-Pock algorithm for problem (1).”
A Generalized Forward-Backward Splitting (2011, background): “In preparing a ﬁrst draft of this manuscript, we became aware that other authors [26, 28, 77] have independently and concurrently developed primal-dual algorithms to solve problems that encompass the one we consider here.”
Learning multiple visual tasks while discovering their structure (2015, methodology): “2 (Convergence of Sparse Kernel MTL, [26, 7]).”
A Dynamical System Associated with the Fixed Points Set of a Nonexpansive Operator (2014, neutral): “We also refer to [9,10,24] for more insights into the outstanding role played by the discrete forward-backward algorithm in connection to the solving of complexly structured monotone inclusion problems.”
Inertial Douglas-Rachford splitting for monotone inclusion problems (2014, methodology): “One can also see that the inertial Douglas–Rachford algorithm is faster than other popular primal-dual solvers, among them the forward-backward-forward (FBF) method from [21], and the forwardbackward (FB) method from [36], where in both methods the function h is processed via a forward step.”
A Three-Operator Splitting Scheme and its Optimization Applications (2015, background): “A large variety of recent algorithms [12,26,37] and their generalizations and enhancements [4,7,6,8,16,17, 18,20,28,39] are (skillful) applications of one of the following three operator-splitting schemes: (i) forwardbackward-forward splitting (FBFS) [38], (ii) forward-backward splitting (FBS) [36],”
Warped proximal iterations for monotone inclusions (2019, background): “To address this issue, various splitting strategies have been proposed to handle increasingly complex formulations in which M is a composite operator assembled from several elementary blocks that can be linear operators and monotone operators [5, 7, 9, 10, 11, 12, 17, 18, 21, 22, 30, 37].”
Decentralized consensus optimization with asynchrony and delays (2016, neutral): “We will compare it with its synchronous counterpart (12) (synchronous PG-EXTRA) as well as the proximal gradient descent algorithms (synchronous algorithm (21) and asynchronous algorithm (22)).”
Forward-Douglas–Rachford splitting and forward-partial inverse method for solving monotone inclusions (2012, methodology): “In [35,43] two different methods for solving Problem 6.”
Decentralized Consensus Optimization With Asynchrony and Delays (2016, background): “This paper introduces an asynchronous, decentralized algo-rithm for problem (1) that provably converges to an optimal solution assuming that the next update is performed by a random agent and that communication is subject to arbitrary and possibly unbounded delays.”
Distributed Proximal Splitting Algorithms with Rates and Acceleration (2020, methodology): “On the other hand, the latter encompasses the Condat–Vũ algorithm [22,23], which is not the case of our approach.”
Dualize, Split, Randomize: Fast Nonsmooth Optimization Algorithms (2020, methodology): “V˜u algorithm [13, 14] was designed as a primal–dual instance of forward–backward splitting, for instance.”
Stochastic Approximations and Perturbations in Forward-Backward Splitting for Monotone Operators (2015, background): “…stress that a major motivation for studying the forward-backward algorithm is that it can be applied not only to Problem 1.1 per se, but also to systems of coupled monotone inclusions via product space reformulations [2], to strongly monotone composite inclusions problems via duality arguments…”