A Wiener-Hopf dynamical system for variational inequalities. (English) Zbl 1047.49011

Noor, Muhammad Aslam

N. Z. J. Math. 31, No. 2, 173-182 (2002).

Using the fixed point formulation of the variational inequality problem, which is based on the Wiener-Hopf equation, the author presents a continuous version of the known extragradient type method in the finite-dimensional spaces. The convergence of the method is proved under the assumptions that the cost mapping is pseudomonotone and Lipschitz continuous. However, Theorem 3.3 contains ambiguous conditions which do not allow for evaluating its assertion.

Reviewer: Igor V. Konnov (Kazan)

MSC:

49J40	Variational inequalities
90C33	Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)

Keywords:

variational inequalities; dynamical systems; extragradient methods; Wiener-Hopf equation