Golden ratio algorithms with new stepsize rules for variational inequalities

Abstract

In this paper, we introduce two golden ratio algorithms with new stepsize rules for solving pseudomonotone and Lipschitz variational inequalities in finite dimensional Hilbert spaces. The presented stepsize rules allow the resulting algorithms to work without the prior knowledge of the Lipschitz constant of operator. The first algorithm uses a sequence of stepsizes that is previously chosen, diminishing, and nonsummable, while the stepsizes in the second one are updated at each iteration and by a simple computation. A special point is that the sequence of stepsizes generated by the second algorithm is separated from zero.The convergence and the convergence rate of the proposed algorithms are established under some standard conditions. Also, we give several numerical results to show the behavior of the algorithms in comparison with other algorithms. KEYWORDSLipschitz continuity, projection method, pseudomonotone operator, variational inequality MSC CLASSIFICATION65J15; 65Y05; 47H05; 47J25; 91B50 } .

Tseng methods with inertial for solving inclusion problems and application to image deblurring and image recovery problems

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Generalized Penalty Method for a Class of Variational-hemivariational Inequality

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Strong convergence of new iterative projection methods with regularization for solving monotone variational inequalities in Hilbert spaces

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