A Novel Inertial Projection and Contraction Method for Solving Pseudomonotone Variational Inequality Problems

Cholamjiak, Prasit; Thong, Duong Viet; Cho, Yeol Je

doi:10.1007/s10440-019-00297-7

Cited by 70 publications

(63 citation statements)

References 50 publications

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“…This improves the results of [10,11,44,45] and many other results in this direction. (c) The strong convergence result proved in this paper is more desirable in optimization theory than the weak convergence counterparts; see [3].…”

Section: Remark 38supporting

confidence: 75%

“…In this section, we will test the numerical efficiency of the proposed Algorithm 3.3 by solving some variational inequality problems. We shall compare our method Algorithm 3.3 with other inertial projection contraction methods proposed in [10,11,44]. Our interest is to investigate how the line search process improve the numerical efficiency of Algorithm 3.3.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…Moreover, other authors have further introduced some strong convergence inertial PCM with certain stepsize conditions in real Hilbert spaces; see e.g. [10,18,26,27,39,40,44]. Note that the stepsize conditions in the above methods restrict the applicability of the methods due to the prior estimate of the Lipschitz constant L. In reality, the Lipschitz constant is very difficult to estimate and even when it is estimated, it is often too small and deteriorates the convergence of the methods.…”

Section: Introductionmentioning

confidence: 99%

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Strong convergence inertial projection and contraction method with self adaptive stepsize for pseudomonotone variational inequalities and fixed point problems

Jolaoso

Aphane

2020

J Inequal Appl

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In this paper, we introduce a new inertial self-adaptive projection method for finding a common element in the set of solution of pseudomonotone variational inequality problem and set of fixed point of a pseudocontractive mapping in real Hilbert spaces. The self-adaptive technique ensures the convergence of the algorithm without any prior estimate of the Lipschitz constant. With the aid of Moudafi’s viscosity approximation method, we prove a strong convergence result for the sequence generated by our algorithm under some mild conditions. We also provide some numerical examples to illustrate the accuracy and efficiency of the algorithm by comparing with other recent methods in the literature.

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Section: Remark 38supporting

confidence: 75%

Section: Numerical Experimentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Strong convergence inertial projection and contraction method with self adaptive stepsize for pseudomonotone variational inequalities and fixed point problems

Jolaoso

Aphane

2020

J Inequal Appl

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“…The variational inequality theory is an important tool based on studying a wide class of problems-unilateral and equilibrium problems arising in structural analysis, economics, optimization, operations research, and engineering sciences (see [2][3][4][5][6][7] and the references therein). Several algorithms have been improved for solving variational inequality and related optimization problems (see [6,[8][9][10][11][12][13][14][15] and the references therein). It is well known that x is the solution of the VIP (5) if and only if x is the fixed point of the mapping P C (I − rA), r > 0 (see [4] for details)…”

Section: Pseudo-monotone Ifmentioning

confidence: 99%

A Parallel-Viscosity-Type Subgradient Extragradient-Line Method for Finding the Common Solution of Variational Inequality Problems Applied to Image Restoration Problems

et al. 2020

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In this paper, we study a modified viscosity type subgradient extragradient-line method with a parallel monotone hybrid algorithm for approximating a common solution of variational inequality problems. Under suitable conditions in Hilbert spaces, the strong convergence theorem of the proposed algorithm to such a common solution is proved. We then give numerical examples in both finite and infinite dimensional spaces to justify our main theorem. Finally, we can show that our proposed algorithm is flexible and has good quality for use with common types of blur effects in image recovery.

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“…Then, the sequence generated by (6) weakly converges to a solution of VIP. This method is often called Tseng's extragradient method and has received great attention by researchers due to its convergence speed (see, for example, [25][26][27][28]). Following this research direction, the main challenge is to design novel algorithms that can speed up the convergence rate compared to Algorithms 1-3.…”

Section: Introductionmentioning

confidence: 99%

A Novel Forward-Backward Algorithm for Solving Convex Minimization Problem in Hilbert Spaces

2020

Self Cite

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In this work, we aim to investigate the convex minimization problem of the sum of two objective functions. This optimization problem includes, in particular, image reconstruction and signal recovery. We then propose a new modified forward-backward splitting method without the assumption of the Lipschitz continuity of the gradient of functions by using the line search procedures. It is shown that the sequence generated by the proposed algorithm weakly converges to minimizers of the sum of two convex functions. We also provide some applications of the proposed method to compressed sensing in the frequency domain. The numerical reports show that our method has a better convergence behavior than other methods in terms of the number of iterations and CPU time. Moreover, the numerical results of the comparative analysis are also discussed to show the optimal choice of parameters in the line search.

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A Novel Inertial Projection and Contraction Method for Solving Pseudomonotone Variational Inequality Problems

Cited by 70 publications

References 50 publications

Strong convergence inertial projection and contraction method with self adaptive stepsize for pseudomonotone variational inequalities and fixed point problems

Strong convergence inertial projection and contraction method with self adaptive stepsize for pseudomonotone variational inequalities and fixed point problems

A Parallel-Viscosity-Type Subgradient Extragradient-Line Method for Finding the Common Solution of Variational Inequality Problems Applied to Image Restoration Problems

A Novel Forward-Backward Algorithm for Solving Convex Minimization Problem in Hilbert Spaces

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