Shrinking projection methods involving inertial forward–backward splitting methods for inclusion problems

Khan, Shahrukh Rafi; Suantai, Suthep; Cholamjiak, Watcharaporn

doi:10.1007/s13398-018-0504-1

Cited by 32 publications

(23 citation statements)

References 22 publications

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“…, we may see that Q n+1 can be deleted which implies that (15) reduces to (4). However, the strong assumption that ∑ ∞ n=1 k n u n − u n−1 < +∞ in [7] is no longer needed in our paper.…”

Section: Remarkmentioning

confidence: 99%

“…The study of the special case of inclusion problem (1), where T is accretive and S is µ-inversely strongly accretive, has been a hot topic during the past few years. In particular, the constructions of the iterative algorithms for approximating the zero point of the sum of T and S are focused, see [3][4][5][6][7][8][9][10][11][12] and the references therein. The inertial forward-backward splitting method is one of the important iterative algorithms studied by some authors, see [7][8][9]13,14].…”

Section: Introductionmentioning

confidence: 99%

“…In 2018, Khan et al proposed the following one in which the projection set Q n is deleted (see [7]):…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

New Inertial Forward-Backward Mid-Point Methods for Sum of Infinitely Many Accretive Mappings, Variational Inequalities, and Applications

Shang

Agarwal

2019

Mathematics

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Some new inertial forward-backward projection iterative algorithms are designed in a real Hilbert space. Under mild assumptions, some strong convergence theorems for common zero points of the sum of two kinds of infinitely many accretive mappings are proved. New projection sets are constructed which provide multiple choices of the iterative sequences. Some already existing iterative algorithms are demonstrated to be special cases of ours. Some inequalities of metric projection and real number sequences are widely used in the proof of the main results. The iterative algorithms have also been modified and extended from pure discussion on the sum of accretive mappings or pure study on variational inequalities to that for both, which complements the previous work. Moreover, the applications of the abstract results on nonlinear capillarity systems are exemplified.

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Section: Remarkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

New Inertial Forward-Backward Mid-Point Methods for Sum of Infinitely Many Accretive Mappings, Variational Inequalities, and Applications

Shang

Agarwal

2019

Mathematics

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“…The forward‐backward method based on iteration has been studied by many authors (see, eg, previous studies)…”

Section: Introductionmentioning

confidence: 99%

“…The forward-backward method based on iteration (3) has been studied by many authors (see, eg, previous studies [10][11][12][13][14][15][16][17][18][19][20][21][22][23] In this work, we present a new modified forward-backward splitting method for solving (1) with a new linesearch. The convergence and the complexity are established under suitable conditions.…”

Section: Introductionmentioning

confidence: 99%

On convergence and complexity of the modified forward‐backward method involving new linesearches for convex minimization

Kankam

Pholasa

Cholamjiak

2019

Math Methods in App Sciences

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In optimization theory, convex minimization problems have been intensively investigated in the current literature due to its wide range in applications. A major and effective tool for solving such problem is the forward‐backward splitting algorithm. However, to guarantee the convergence, it is usually assumed that the gradient of functions is Lipschitz continuous and the stepsize depends on the Lipschitz constant, which is not an easy task in practice. In this work, we propose the modified forward‐backward splitting method using new linesearches for choosing suitable stepsizes and discuss the convergence analysis including its complexity without any Lipschitz continuity assumption on the gradient. Finally, we provide numerical experiments in signal recovery to demonstrate the computational performance of our algorithm in comparison to some well‐known methods. Our reports show that the proposed algorithm has a good convergence behavior and can outperform the compared methods.

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Image restorations using a modified relaxed inertial technique for generalized split feasibility problems

Godwin

Izuchukwu

2022

Math Methods in App Sciences

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In this article, we propose a new efficient self‐adaptive method and prove that it converges strongly to a minimum‐norm solution of a generalized split feasibility problem in real Hilbert spaces. The proposed method is derived from a definite discrete dynamical system in time, which combines both the relaxation and inertial techniques for the purpose of increasing the rate of convergence of the iterative scheme. Furthermore, the method requires the monotonicity and Lipschitz continuity condition of the underlying single‐valued cost operator A$$ A $$, and it employs some simple self‐adaptive stepsizes that are generated at each iteration by some easy computations. As a by‐product, we obtain methods for solving other classes of generalized split feasibility problems in real Hilbert spaces. Two major merits of our scheme in solving image restoration problems over related schemes are the higher signal‐to‐noise ratio value and lower CPU time for generating recovered images. Finally, we analyze our methods with different related strong convergent methods in the literature.

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Shrinking projection methods involving inertial forward–backward splitting methods for inclusion problems

Cited by 32 publications

References 22 publications

New Inertial Forward-Backward Mid-Point Methods for Sum of Infinitely Many Accretive Mappings, Variational Inequalities, and Applications

New Inertial Forward-Backward Mid-Point Methods for Sum of Infinitely Many Accretive Mappings, Variational Inequalities, and Applications

On convergence and complexity of the modified forward‐backward method involving new linesearches for convex minimization

Image restorations using a modified relaxed inertial technique for generalized split feasibility problems

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