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Álvarez, Felipe; Attouch, Hédy

doi:10.1023/a:1011253113155

Cited by 565 publications

(115 citation statements)

References 10 publications

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“…where x k is the current iteration and λ k is a regularization parameter. Attouch and Alvarez [2] applied an inertial technique to (1.3) to develop an inertial proximal method for solving(1.2). It works as follows.…”

Section: 2)mentioning

confidence: 99%

Inertial accelerated algorithms for solving a split feasibility problem

Dang¹,

Sun²,

Xu³

2017

Journal of Industrial &Amp; Management Optimization

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Inspired by the inertial proximal algorithms for finding a zero of a maximal monotone operator, in this paper, we propose two inertial accelerated algorithms to solve the split feasibility problem. One is an inertial relaxed-CQ algorithm constructed by applying inertial technique to a relaxed-CQ algorithm, the other is a modified inertial relaxed-CQ algorithm which combines the KM method with the inertial relaxed-CQ algorithm. We prove their asymptotical convergence under some suitable conditions. Numerical results are reported to show the effectiveness of the proposed algorithms.

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Section: 2)mentioning

confidence: 99%

Inertial accelerated algorithms for solving a split feasibility problem

Dang¹,

Sun²,

Xu³

2017

Journal of Industrial &Amp; Management Optimization

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“…it was proved that x n converges strongly to a point z = Q(u) under some mild conditions, where Q is the sunny nonexpansive retraction. Inertial extrapolation is an important technique to speed up the convergence rate [11][12][13][14]. Recently, the fast-iterative algorithms by using inertial extrapolation studied by some authors [15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Convergence Theorems for Modified Inertial Viscosity Splitting Methods in Banach Spaces

Pan

Wang

2019

Mathematics

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In this article, we study a modified viscosity splitting method combined with inertial extrapolation for accretive operators in Banach spaces and then establish a strong convergence theorem for such iterations under some suitable assumptions on the sequences of parameters. As an application, we extend our main results to solve the convex minimization problem. Moreover, the numerical experiments are presented to support the feasibility and efficiency of the proposed method.

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“…Inertial proximal methods go back to [1, 2], where it has been noticed that the discretization of a differential system of second order in time gives rise to a generalization of the classical proximal-point algorithm. The main feature of the inertial proximal algorithm is that the next iterate is defined by using the last two iterates.…”

Section: Introductionmentioning

confidence: 99%

Inertial proximal alternating minimization for nonconvex and nonsmooth problems

Zhang

2017

J Inequal Appl

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In this paper, we study the minimization problem of the type , where f and g are both nonconvex nonsmooth functions, and R is a smooth function we can choose. We present a proximal alternating minimization algorithm with inertial effect. We obtain the convergence by constructing a key function H that guarantees a sufficient decrease property of the iterates. In fact, we prove that if H satisfies the Kurdyka-Lojasiewicz inequality, then every bounded sequence generated by the algorithm converges strongly to a critical point of L.

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Cited by 565 publications

References 10 publications

Inertial accelerated algorithms for solving a split feasibility problem

Inertial accelerated algorithms for solving a split feasibility problem

Convergence Theorems for Modified Inertial Viscosity Splitting Methods in Banach Spaces

Inertial proximal alternating minimization for nonconvex and nonsmooth problems

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