Convergence analysis of a projection algorithm for variational inequality problems

Biao Qu, Changyu Wang and Fanwen Meng ()
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Biao Qu: Qufu Normal University
Changyu Wang: Qufu Normal University
Fanwen Meng: Dalian Maritime University

Journal of Global Optimization, 2020, vol. 76, issue 2, No 10, 433-452

Abstract: Abstract In this paper, we propose a projection based Newton-type algorithm for solving the variational inequality problems. A comprehensive study is conducted to analyze both global and local convergence properties of the algorithm. In particular, the algorithm is shown to be of superlinear convergence when the solution is a regular point. In addition, when the Jacobian matrix of the underlying function is positive definite at the solution or the solution is a non-degenerate point, the algorithm still possesses its superlinear convergence. Compared to the relevant projection algorithms in literature, the proposed algorithm is of remarkable advantages in terms of its generalization and favorable convergence properties under relaxed assumptions.

Keywords: Variational inequality problem; Global convergence; Local convergence rate; Regular solution; 90C33; 65K15; 49M15 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10898-019-00848-0

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