Backward-Forward-Reflected-Backward Splitting for Three Operator Monotone Inclusions

Rieger, Janosch; Tam, Matthew K.

doi:10.1016/j.amc.2020.125248

Cited by 21 publications

(28 citation statements)

References 13 publications

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“…and thus, solving (27) boils down to computing the resolvent at q of the sum of the three maximally monotone operators A := N A , B := N B and T := 1 ρ (Id −P C ), with T being 1 ρ -cocoercive (see, e.g., [7,Corollary 12.31]).…”

Section: Corollary 35 Let B : H ⇒ H Be a Maximally Monotone Operator ...mentioning

confidence: 99%

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A Direct Proof of Convergence of Davis–Yin Splitting Algorithm Allowing Larger Stepsizes

Artacho

David

2022

Set-Valued Var. Anal

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This note is devoted to the splitting algorithm proposed by Davis and Yin (Set-valued Var. Anal. 25(4), 829–858, 2017) for computing a zero of the sum of three maximally monotone operators, with one of them being cocoercive. We provide a direct proof that guarantees its convergence when the stepsizes are smaller than four times the cocoercivity constant, thus doubling the size of the interval established by Davis and Yin. As a by-product, the same conclusion applies to the forward-backward splitting algorithm. Further, we use the notion of “strengthening” of a set-valued operator to derive a new splitting algorithm for computing the resolvent of the sum. Last but not least, we provide some numerical experiments illustrating the importance of appropriately choosing the stepsize and relaxation parameters of the algorithms.

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Section: Corollary 35 Let B : H ⇒ H Be a Maximally Monotone Operator ...mentioning

confidence: 99%

“…Only recently, three-operator splitting algorithms have been developed [18,21,[27][28][29]. This note is devoted to one of them, which was introduced by Damek Davis and Wotao Yin in [18], and is commonly referred as Davis-Yin splitting algorithm.…”

Section: Introductionmentioning

confidence: 99%

A Direct Proof of Convergence of Davis–Yin Splitting Algorithm Allowing Larger Stepsizes

Artacho

David

2022

Set-Valued Var. Anal

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“…Their algorithms are however significantly different from Algorithm 1, and hence all worthy of investigation. Note finally that we base our algorithm on Davis-Yin splitting for its simplicity, although we could have chosen other three-operator splitting methods [18][19][20][21].…”

Section: Proposed Algorithmmentioning

confidence: 99%

“…Their goal is to split the optimization process into elementary operations like gradient steps, "simple" proximity operators, and linear operators. Proximal algorithms can be classified in primal methods [12][13][14][15][16][17][18][19][20][21] and primal-dual methods [22][23][24][25]. The main difference is that the latter do not need to invert the linear operators involved in the optimization problem, even though the former may converge faster when such an inversion can be efficiently computed.…”

Section: Introductionmentioning

confidence: 99%

“…The proposed algorithm can activate smooth functions via their gradients, and allows for linear operators in nonsmooth functions. This distinguishes it from many other primal proximal methods, which can only activate smooth functions through their proximity operator [14,15], or do not allow for linear operators in nonsmooth functions [18][19][20][21]. Moreover, unlike primaldual proximal methods [23], the proposed algorithm only requires to set a single stepsize, and can be accelerated with great effect via Anderson extrapolation [26] (see Section 3).…”

Section: Introductionmentioning

confidence: 99%

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Yapa: Accelerated Proximal Algorithm for Convex Composite Problems

Chierchia

Gheche

2021

ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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Proximal splitting methods are standard tools for nonsmooth optimization. While primal-dual methods have become very popular in the last decade for their flexibility, primal methods may still be preferred for two reasons: acceleration schemes are more effective, and only a single stepsize is required. In this paper, we propose a primal proximal method derived from a three-operator splitting in a product space and accelerated with Anderson extrapolation. The proposed algorithm can activate smooth functions via their gradients, and allows for linear operators in nonsmooth functions. Numerical results show the good performance of our algorithm with respect to well-established modern optimization methods.

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A product space reformulation with reduced dimension for splitting algorithms

Campoy

2022

Comput Optim Appl

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In this paper we propose a product space reformulation to transform monotone inclusions described by finitely many operators on a Hilbert space into equivalent two-operator problems. Our approach relies on Pierra’s classical reformulation with a different decomposition, which results in a reduction of the dimension of the outcoming product Hilbert space. We discuss the case of not necessarily convex feasibility and best approximation problems. By applying existing splitting methods to the proposed reformulation we obtain new parallel variants of them with a reduction in the number of variables. The convergence of the new algorithms is straightforwardly derived with no further assumptions. The computational advantage is illustrated through some numerical experiments.

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Backward-Forward-Reflected-Backward Splitting for Three Operator Monotone Inclusions

Cited by 21 publications

References 13 publications

A Direct Proof of Convergence of Davis–Yin Splitting Algorithm Allowing Larger Stepsizes

A Direct Proof of Convergence of Davis–Yin Splitting Algorithm Allowing Larger Stepsizes

Yapa: Accelerated Proximal Algorithm for Convex Composite Problems

A product space reformulation with reduced dimension for splitting algorithms

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