Inertial iterative algorithms for common solution of variational inequality and system of variational inequalities problems

Sahu, D. R.; Singh, Amit

doi:10.1007/s12190-020-01395-8

“…respectively. We will say: (i) (31) is the relaxed inertial Mann iteration based Korpelevich's extragradient method (RIM-KEM), (ii) ( 32) is inertial Korpelevich's extragradient method (I-KEM), (iii) (33) is the relaxed inertial normal S-iteration based Korpelevich's extragradient method (RInS-KEM).…”

Section: Applications To Pseudo-monotone Variational Inequality Problemsmentioning

confidence: 99%

“…Theorem 4.3 Let C be a nonempty closed convex subset of X and F : X → X a pseudo-monotone and L-Lipschitz continuous operator such that Ω[VI(C, F )] = ∅. For λ ∈ (0, 1/L) and x 0 = x 1 ∈ C, let {x n } be a sequence in X generated by RInS-KEM (33) or RInS-SEM (39), where sequences {α n } and {θ n } satisfy the conditions (C1), (C2) and (C5) with κ = (1 − λL)/2. Then {x n } converges weakly to an element of Ω[VI(C, F )].…”

Section: Applications To Pseudo-monotone Variational Inequality Problemsmentioning

confidence: 99%

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The main strategy of this paper is intended to speed up the convergence of the inertial Mann iterative method and further speed up it through the normal S-iterative method for a certain class of nonexpansive type operators that are linked with variational inequality problems. Our new convergence theory permits us to settle down the difficulty of unification of Korpelevich's extragradient method, Tseng's extragardient method, and subgardient extragardient method for solving variational inequality problems through an auxiliary algorithmic operator, which is associated with seed operator. The paper establishes an interesting fact that the relaxed inertial normal S-iterative extragradient methods do influence much more on convergence behaviour. Finally, the numerical experiments are carried out to illustrate that the relaxed inertial iterative methods, in particular the relaxed inertial normal S-iterative extragradient methods, may have a number of advantages over other methods in computing solutions of variational inequality problems in many cases.

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“…) and θ n = .9δ(ε) for algorithms RIM-KEM(31) and RIM-SEM(37), where δ is defined in (12) and ε = (1 + κ E − b)/b. • α n = b = .961(1 + κ E ) and θ n = .9δ(E) in algorithms RInS-KEM (33) and RInS-SEM (39),…”

Section: Example 41 Letmentioning

confidence: 99%

“…Let C be a nonempty closed convex subset of X and F : X → X a pseudo-monotone and L-Lipschitz continuous operator such that Ω[VI(C, F )] = ∅. For λ ∈ (0, 1/L) and x 0 = x 1 ∈ C, let {x n } be a sequence in X generated by RInS-KEM(33) or RInS-SEM (39), where sequences {α n } and {θ n } satisfy the conditions (C1), (C2) and (C5) with κ = (1 − λL)/2. Then {x n } converges weakly to an element of Ω[VI(C, F )].…”

mentioning

confidence: 99%

A unified framework for three accelerated extragradient methods and further acceleration for variational inequality problems

Sahu

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2021

Preprint

Self Cite

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The main strategy of this paper is intended to speed up the convergence of the inertial Mann iterative method and further speed up it through the normal S-iterative method for a certain class of nonexpansive type operators that are linked with variational inequality problems. Our new convergence theory permits us to settle down the difficulty of unification of Korpelevich's extragradient method, Tseng's extragardient method, and subgardient extragardient method for solving variational inequality problems through an auxiliary algorithmic operator, which is associated with seed operator. The paper establishes an interesting fact that the relaxed inertial normal S-iterative extragradient methods do influence much more on convergence behaviour. Finally, the numerical experiments are carried out to illustrate that the relaxed inertial iterative methods, in particular the relaxed inertial normal S-iterative extragradient methods, may have a number of advantages over other methods in computing solutions of variational inequality problems in many cases.

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An inertial Bregman generalized alternating direction method of multipliers for nonconvex optimization

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Inertial iterative algorithms for common solution of variational inequality and system of variational inequalities problems

Cited by 7 publications

References 30 publications

A unified framework for three accelerated extragradient methods and further acceleration for variational inequality problems

A unified framework for three accelerated extragradient methods and further acceleration for variational inequality problems

A unified framework for three accelerated extragradient methods and further acceleration for variational inequality problems

An inertial Bregman generalized alternating direction method of multipliers for nonconvex optimization

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