A Strong Convergence Theorem for Solving Pseudo-monotone Variational Inequalities Using Projection Methods

Jolaoso, Lateef Olakunle; Taiwo, Adeolu; Alakoya, Timilehin Opeyemi; Mewomo, Oluwatosin Temitope

doi:10.1007/s10957-020-01672-3

Cited by 76 publications

(29 citation statements)

References 44 publications

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“…Assume that (A1), (A2), (A3), (B1), and (B2) hold. Let the sequence { } α n be chosen such that it satisfies (8). Then, the sequence { }…”

Section: Lemma 34 Let { }mentioning

confidence: 99%

“…The solution set of VIP (1) is denoted by ( ) VI C A , . Variational inequality theory is an important tool in economics, engineering, mathematical programming, transportation, and in other fields (see, for example, [1][2][3][4][5][6][7][8]). Many numerical methods have been constructed for solving variational inequalities and related optimization problems, see [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] and references therein.…”

Section: Introductionmentioning

confidence: 99%

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Two modifications of the inertial Tseng extragradient method with self-adaptive step size for solving monotone variational inequality problems

Alakoya

Jolaoso

2020

Demonstratio Mathematica

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In this work, we introduce two new inertial-type algorithms for solving variational inequality problems (VIPs) with monotone and Lipschitz continuous mappings in real Hilbert spaces. The first algorithm requires the computation of only one projection onto the feasible set per iteration while the second algorithm needs the computation of only one projection onto a half-space, and prior knowledge of the Lipschitz constant of the monotone mapping is not required in proving the strong convergence theorems for the two algorithms. Under some mild assumptions, we prove strong convergence results for the proposed algorithms to a solution of a VIP. Finally, we provide some numerical experiments to illustrate the efficiency and advantages of the proposed algorithms.

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“…Assume that (A1), (A2), (A3), (B1), and (B2) hold. Let the sequence { } α n be chosen such that it satisfies (8). Then, the sequence { }…”

Section: Lemma 34 Let { }mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Two modifications of the inertial Tseng extragradient method with self-adaptive step size for solving monotone variational inequality problems

Alakoya

Jolaoso

2020

Demonstratio Mathematica

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“…If A is η-strongly monotone and L-Lipschitz continuous, then A is η L 2 -inverse strongly monotone. Also, we note that every monotone operator is pseudomonotone but the converse is not true; see, for instance [25,26]. If α = 1, then T is called a nonexpansive mapping, (ii) a κ-strictly pseudocontraction, if there exists κ…”

Section: Preliminariesmentioning

confidence: 99%

“…The authors also proved that the sequence {x n } generated by the SEGM converges weakly to a solution of the VIP (1.1) if the stepsize condition λ ∈ (0, 1 L ). Several modifications of the EGM and SEGM have been introduced by many authors; see for instance [12,22,[24][25][26][41][42][43]. Recently, He [17] modified the EGM and introduced a projection and contraction method (PCM) which requires only a single projection per each iteration as follows:…”

Section: Introductionmentioning

confidence: 99%

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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“…Let C be a nonempty subset of intdom f . A mapping T : C → intdom f is said to be Bregman Quasi-Nonexpansive (BQNE) (see [26]) if Fix(T ) = / 0 and…”

Section: Preliminariesmentioning

confidence: 99%

A subgradient extragradient algorithm for solving split equilibrium and fixed point problems in reflexive Banach spaces

2020

J. Nonlinear Funct. Anal.

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A Strong Convergence Theorem for Solving Pseudo-monotone Variational Inequalities Using Projection Methods

Cited by 76 publications

References 44 publications

Two modifications of the inertial Tseng extragradient method with self-adaptive step size for solving monotone variational inequality problems

Two modifications of the inertial Tseng extragradient method with self-adaptive step size for solving monotone variational inequality problems

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

A subgradient extragradient algorithm for solving split equilibrium and fixed point problems in reflexive Banach spaces

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