Modified projection method for strongly pseudomonotone variational inequalities

Khanh, Pham Duy; Vuong, Phan Tu

doi:10.1007/s10898-013-0042-5

Cited by 97 publications

(46 citation statements)

References 5 publications

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“…It is easily seen that r attains the minimum when λ = γ Q 2 . (ii) Corollary 1 is a generalization of the corresponding result for variational inequalities in [16].…”

Section: Algorithm 2 (One-projection Algorithm)mentioning

confidence: 79%

Splitting extragradient-like algorithms for strongly pseudomonotone equilibrium problems

Pham

Trinh

2016

Numer Algor

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In this paper, two splitting extragradient-like algorithms for solving strongly pseudomonotone equilibrium problems given by a sum of two bifunctions are proposed. The convergence of the proposed methods is analyzed and the R-linear rate of convergence under suitable assumptions on bifunctions is established. Moreover, a noisy data case, when a part of the bifunction is contaminated by errors, is studied. Finally, some numerical experiments are given to demonstrate the efficiency of our algorithms.

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“…It is easily seen that r attains the minimum when λ = γ Q 2 . (ii) Corollary 1 is a generalization of the corresponding result for variational inequalities in [16].…”

Section: Algorithm 2 (One-projection Algorithm)mentioning

confidence: 79%

Splitting extragradient-like algorithms for strongly pseudomonotone equilibrium problems

Pham

Trinh

2016

Numer Algor

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“…We only prove (4.14). For the proof of (4.13), see [4]. Since e n = γ n (F (x n+1 ) − F (x n )), it follows from (4.5) that…”

Section: 2mentioning

confidence: 99%

Finite convergence analysis and weak sharp solutions for variational inequalities

2016

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Abstract. In this paper, we study the weak sharpness of the solution set of variational inequality problem (in short, VIP) and the finite convergence property of the sequence generated by some algorithm for finding the solutions of VIP. In particular, we give some characterizations of weak sharpness of the solution set of VIP without considering the primal or dual gap function. We establish an abstract result on the finite convergence property for a sequence generated by some iterative methods. We then apply such abstract result to discuss the finite termination property of the sequence generated by proximal point method, exact proximal point method and gradient projection method. We also give an estimate on the number of iterates by which the sequence converges to a solution of the VIP.

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“…Interested readers may refer to some recent articles that propose algorithms with variable step sizes which are independent of factorials of the underlying operator and Lipschitz constant (Refs. [28][29][30][31]). The question now is, can we have an iterative scheme involving a more general class of operators with a strong convergence and self-adaptive step size?…”

Section: Introductionmentioning

confidence: 99%

Inertial Iterative Schemes with Variable Step Sizes for Variational Inequality Problem Involving Pseudomonotone Operator

2020

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Two inertial subgradient extragradient algorithms for solving variational inequality problems involving pseudomonotone operator are proposed in this article. The iterative schemes use self-adaptive step sizes which do not require the prior knowledge of the Lipschitz constant of the underlying operator. Furthermore, under mild assumptions, we show the weak and strong convergence of the sequences generated by the proposed algorithms. The strong convergence in the second algorithm follows from the use of viscosity method. Numerical experiments both in finite- and infinite-dimensional spaces are reported to illustrate the inertial effect and the computational performance of the proposed algorithms in comparison with the existing state of the art algorithms.

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Modified projection method for strongly pseudomonotone variational inequalities

Cited by 97 publications

References 5 publications

Splitting extragradient-like algorithms for strongly pseudomonotone equilibrium problems

Splitting extragradient-like algorithms for strongly pseudomonotone equilibrium problems

Finite convergence analysis and weak sharp solutions for variational inequalities

Inertial Iterative Schemes with Variable Step Sizes for Variational Inequality Problem Involving Pseudomonotone Operator

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