Single projection method for pseudo-monotone variational inequality in Hilbert spaces

Shehu, Yekini; Dong, Qiao-Li; Jiang, Dan

doi:10.1080/02331934.2018.1522636

Cited by 108 publications

(32 citation statements)

References 49 publications

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“…with C = x ∈ R 2 : -10 ≤ x i ≤ 10 . The bifunction is not monotone on C but pseudomonotone (for more details see p. 10, [59,60]). Figure 9 illustrates the numerical results of comparison of Algorithm 2 with two other algorithms, with x -1 = (5, 5) T and x 0 = (10, 10) T .…”

Section: Nash-cournot Equilibrium Models Of Electricity Marketsmentioning

confidence: 99%

Weak convergence of explicit extragradient algorithms for solving equilibirum problems

et al. 2019

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This paper aims to propose two new algorithms that are developed by implementing inertial and subgradient techniques to solve the problem of pseudomonotone equilibrium problems. The weak convergence of these algorithms is well established based on standard assumptions of a cost bi-function. The advantage of these algorithms was that they did not need a line search procedure or any information on Lipschitz-type bifunction constants for step-size evaluation. A practical explanation for this is that they use a sequence of step-sizes that are updated at each iteration based on some previous iterations. For numerical examples, we discuss two well-known equilibrium models that assist our well-established convergence results, and we see that the suggested algorithm has a competitive advantage over time of execution and the number of iterations.

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Section: Nash-cournot Equilibrium Models Of Electricity Marketsmentioning

confidence: 99%

Weak convergence of explicit extragradient algorithms for solving equilibirum problems

et al. 2019

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“…According to the condition of the convergence of Halpern-type algorithm, we assume that lim k→∞ τ k = 0 and ∞ k=1 τ k = ∞. As shown in [30], F is monotone and L-Lipschitz-continuous with L = 2. Let f (x(t), y(t)) = Fx(t), y(t)x(t) , g(x)(t) = 1 2 x(t) 2 and (Ax)(t) = 3x(t) for all x ∈ H.…”

Section: Numerical Examplesmentioning

confidence: 99%

Some algorithms for classes of split feasibility problems involving paramonotone equilibria and convex optimization

Dong

Kitkuan

et al. 2019

J Inequal Appl

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In this paper, we first introduce a new algorithm which involves projecting each iteration to solve a split feasibility problem with paramonotone equilibria and using unconstrained convex optimization. The strong convergence of the proposed algorithm is presented. Second, we also revisit this split feasibility problem and replace the unconstrained convex optimization by a constrained convex optimization. We introduce some algorithms for two different types of objective function of the constrained convex optimization and prove some strong convergence results of the proposed algorithms. Third, we apply our algorithms for finding an equilibrium point with minimal environmental cost for a model in electricity production. Finally, we give some numerical results to illustrate the effectiveness and advantages of the proposed algorithms.

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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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Single projection method for pseudo-monotone variational inequality in Hilbert spaces

Cited by 108 publications

References 49 publications

Weak convergence of explicit extragradient algorithms for solving equilibirum problems

Weak convergence of explicit extragradient algorithms for solving equilibirum problems

Some algorithms for classes of split feasibility problems involving paramonotone equilibria and convex optimization

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

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