A doublestep extragradient method for solving a problem of the management of resources

Zykina, A. V.; Melen’chuk, N. V.

doi:10.3103/s0146411611070170

Cited by 3 publications

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“…The computational performance of all the two-step algorithms over the classical extragradient method have been illustrated by several numerical experiments for solving resource management problems in [26,28] and others in [20].…”

Section: Introductionmentioning

confidence: 99%

Multi-Step Algorithms for Solving Equilibrium Problems

Ánh

Hieu

2018

Mathematical Modelling and Analysis

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The paper introduces and analysizes the convergence of two multi-step proximal-like algorithms for pseudomonotone and Lipschitz-type continuous equilibrium problems in a real Hilbert space. The algorithms are combinations between the multi-step proximal-like method and Mann or Halpern iterations. The weakly and strongly convergent theorems are established with the prior knowledge of two Lipschitz-type continuous constants. Moreover, by choosing two sequences of suitable stepsizes, we also show that the multi-step proximal-like algorithm for strongly pseudomonotone and Lipschitz-type continuous equilibrium problems where the construction of solution approximations and the establishing of its convergence do not require the prior knowledge of strongly pseudomonotone and Lipschitz-type continuous constants of bifunctions. Finally, several numerical examples are reported to illustrate the convergence and the performance of the proposed algorithms over classical extragradient-like algorithms.

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Section: Introductionmentioning

confidence: 99%

Multi-Step Algorithms for Solving Equilibrium Problems

Ánh

Hieu

2018

Mathematical Modelling and Analysis

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“…Furthermore, conditions are given on F to obtain the convergence in a finite number of iterations [24]. Finally, let us also mention that the two-step extragradient method has been applied for solving a resource management problem (see [22,23]).…”

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confidence: 99%