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Set-valued implicit Wiener-Hopf equations and generalized strongly nonlinear quasivariational inequalities. (English) Zbl 0912.49007

In this paper, it is shown that a class of generalized strongly nonlinear quasivariational inequalities are equivalent to a class of set-valued implicit Wiener-Hopf equations essentially using the technique of P. Shi [Proc. Am. Math. Soc. 111, No. 2, 339-344 (1991; Zbl 0881.35049)] and M. A. Noor [J. Optimization Theory Appl. 79, No. 1, 197-206 (1993; Zbl 0799.49010)]. This alternative formulation is used to suggest an iterative method for solving variational inequalities and related problems.

MSC:

49J40 Variational inequalities
65J15 Numerical solutions to equations with nonlinear operators
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
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