A Modified Projected Gradient Method for Monotone Variational Inequalities

Yang, Jun; Liu, Hongwei

doi:10.1007/s10957-018-1351-0

Cited by 59 publications

(31 citation statements)

References 9 publications

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“…This is probably the most important feature of the proposed algorithm. When F is Lipschitz, there are some other methods without linesearch that do not require to know the Lipschitz constant, e.g., [58]. However, such methods use nonincreasing stepsizes, which is rather restrictive.…”

Section: Algorithm 1 Adaptive Golden Ratio Algorithmmentioning

confidence: 99%

Golden ratio algorithms for variational inequalities

2019

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The paper presents a fully adaptive algorithm for monotone variational inequalities. In each iteration the method uses two previous iterates for an approximation of the local Lipschitz constant without running a linesearch. Thus, every iteration of the method requires only one evaluation of a monotone operator F and a proximal mapping g. The operator F need not be Lipschitz continuous, which also makes the algorithm interesting in the area of composite minimization. The method exhibits an ergodic O(1/k) convergence rate and R-linear rate under an error bound condition. We discuss possible applications of the method to fixed point problems as well as its different generalizations.Keywords. variational inequality · first-order methods · linesearch · saddle point problem · composite minimization · fixed point problem MSC2010. 47J20, 65K10, 65K15, 65Y20, 90C33

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Section: Algorithm 1 Adaptive Golden Ratio Algorithmmentioning

confidence: 99%

Golden ratio algorithms for variational inequalities

2019

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“…Example 2 Let H = R m . We consider a classical problem [23,24]. The feasible set is C = R m and F : R m → R m is a linear operator in the form…”

Section: Numerical Experimentsmentioning

confidence: 99%

Inertial hybrid algorithm for variational inequality problems in Hilbert spaces

Tian

Jiang

2020

J Inequal Appl

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For a variational inequality problem, the inertial projection and contraction method have been studied. It has a weak convergence result. In this paper, we propose a strong convergence iterative method for finding a solution of a variational inequality problem with a monotone mapping by projection and contraction method and inertial hybrid algorithm. Our result can be used to solve other related problems in Hilbert spaces. MSC: 58E35; 47H09; 65J15

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“…Under appropriate conditions, there are two general approaches for solving the variational inequality problem, one is the regularized method and the other is the projection method. Many projection-type algorithms for solving the variational inequalities problem have been proposed and analyzed by many authors [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. The gradient method is the simplest algorithm in which only one projection on feasible set is performed, and the convergence of the method requires a strongly monotonicity.…”

Section: Introductionmentioning

confidence: 99%

A subgradient extragradient algorithm for solving monotone variational inequalities in Banach spaces

2020

J Inequal Appl

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In this paper, we introduce an algorithm for solving classical variational inequalities problem with Lipschitz continuous and monotone mapping in Banach space. We modify the subgradient extragradient methods with a new and simple iterative step size, the strong convergence of algorithm is established without the knowledge of the Lipschitz constant of the mapping. Finally, a numerical experiment is presented to show the efficiency and advantage of the proposed algorithm. Our results generalize some of the work in Hilbert spaces to Banach spaces.

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A Modified Projected Gradient Method for Monotone Variational Inequalities

Cited by 59 publications

References 9 publications

Golden ratio algorithms for variational inequalities

Golden ratio algorithms for variational inequalities

Inertial hybrid algorithm for variational inequality problems in Hilbert spaces

A subgradient extragradient algorithm for solving monotone variational inequalities in Banach spaces

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