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Modified inertial projection and contraction algorithms for solving variational inequality problems with non-Lipschitz continuous operators. (English) Zbl 1496.47104

Summary: In this paper, we present four modified inertial projection and contraction methods to solve the variational inequality problem with a pseudo-monotone and non-Lipschitz continuous operator in real Hilbert spaces. Strong convergence theorems of the proposed algorithms are established without the prior knowledge of the Lipschitz constant of the operator. Several numerical experiments and the applications to optimal control problems are provided to verify the advantages and efficiency of the proposed algorithms.

MSC:

47J25 Iterative procedures involving nonlinear operators
47J20 Variational and other types of inequalities involving nonlinear operators (general)
49J40 Variational inequalities
65K15 Numerical methods for variational inequalities and related problems
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