A projection algorithm for solving pseudomonotone equilibrium problems and it's application to a class of bilevel equilibria

Dinh, Bui Van; Mưu, Lê Dũng

doi:10.1080/02331934.2013.773329

Cited by 21 publications

(25 citation statements)

References 16 publications

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“…In this example, we compare the performance of our algorithms with Armijo line search algorithm (shortly Algorithm ALS) (Algorith 1 in [11]). Consider the following mixed variational inequalities [24,25]:…”

Section: Example 5 (Applications To Mixed Variational Inequalities)mentioning

confidence: 99%

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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Section: Example 5 (Applications To Mixed Variational Inequalities)mentioning

confidence: 99%

Splitting extragradient-like algorithms for strongly pseudomonotone equilibrium problems

Pham

Trinh

2016

Numer Algor

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“…Lemma 2.8 (Dinh & Muu, 2015;Solodov & Svaiter, 1999) Suppose that x ∈ C and u = P C∩H z (x). Then, Lemma 2.9 (Maingé, 2008b) and, for all k ≥ k 0 , the following two inequalities hold: (1) If y k = x k , then x k is a solution to EP(C, f ).…”

Section: Lemma 27 Suppose the Bifunction F Satisfies The Assumptionsmentioning

confidence: 99%

An algorithm for variational inequalities with equilibrium and fixed point constraints

Dinh

2015

Cogent Mathematics

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In this paper, we propose a new hybrid extragradient-viscosity algorithm for solving variational inequality problems, where the constraint set is the common elements of the set of solutions of a pseudomonotone equilibrium problem and the set of fixed points of a demicontractive mapping. Using the hybrid extragradientviscosity method and combining with hybrid plane cutting techniques, we obtain the algorithm for this problem. Under certain conditions on parameters, the convergence of the iteration sequences generated by the algorithms is obtained.

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“…Letting y = y n in (16) and y = y n in (17) and adding them, we get ⟨∇K n (y n ) − ∇K n ( n ), y n − n ⟩ ≤ 0.…”

Section: Corollarymentioning

confidence: 99%

“…To dominate this difficulty, researchers applied the linesearch method to afford algorithms for solving ( EP ). ()…”

Section: Introductionmentioning

confidence: 99%

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Extragradient and linesearch methods for solving split feasibility problems in Hilbert spaces

Jouymandi

Moradlou

2019

Math Methods in App Sciences

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Utilizing the Tikhonov regularization method and extragradient and linesearch methods, some new extragradient and linesearch algorithms have been introduced in the framework of Hilbert spaces. In the presented algorithms, the convexity of optimization subproblems is assumed, which is weaker than the strong convexity assumption that is usually supposed in the literature, and also, the auxiliary equilibrium problem is not used. Some strong convergence theorems for the sequences generated by these algorithms have been proven. It has been shown that the limit point of the generated sequences is a common element of the solution set of an equilibrium problem and the solution set of a split feasibility problem in Hilbert spaces. To illustrate the usability of our results, some numerical examples are given. Optimization subproblems in these examples have been solved by FMINCON toolbox in MATLAB.

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A projection algorithm for solving pseudomonotone equilibrium problems and it's application to a class of bilevel equilibria

Cited by 21 publications

References 16 publications

Splitting extragradient-like algorithms for strongly pseudomonotone equilibrium problems

Splitting extragradient-like algorithms for strongly pseudomonotone equilibrium problems

An algorithm for variational inequalities with equilibrium and fixed point constraints

Extragradient and linesearch methods for solving split feasibility problems in Hilbert spaces

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