Solving quasimonotone and non-monotone variational inequalities

V. A. Uzor (), T. O. Alakoya (), O. T. Mewomo () and A. Gibali ()
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V. A. Uzor: University of KwaZulu-Natal
T. O. Alakoya: University of KwaZulu-Natal
O. T. Mewomo: University of KwaZulu-Natal
A. Gibali: Braude College of Engineering

Mathematical Methods of Operations Research, 2023, vol. 98, issue 3, No 6, 498 pages

Abstract: Abstract We present a simple iterative method for solving quasimonotone as well as classical variational inequalities without monotonicity. Strong convergence analysis is given under mild conditions and thus generalize the few existing results that only present weak convergence methods under restrictive assumptions. We give finite and infinite dimensional numerical examples to compare and illustrate the simplicity and computational advantages of the proposed scheme.

Keywords: Projection and contraction method; Quasimonotone variational inequality problem; Inertial technique; Self-adaptive step size; 65K15; 47J25; 47H05; 47H10 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s00186-023-00846-9

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