Some recent advances in variational inequalities. I: Basic concepts. (English) Zbl 0886.49004

This is a survey paper on various algorithms in Hilbert spaces for the solution of variational inequalities associated to indicator functions and other related problems (complementarity problems, quasivariational inequalities, general nonlinear variational inequalities, variational-like inequalities). In each case, the author discusses several approximation techniques: projection methods, Wiener-Hopf equation approach, auxiliary principles, gap functions, parallel implementation. The exposition is well organised and clear and the covered literature is very rich, including many personal contributions.


49J40 Variational inequalities
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
35J85 Unilateral problems; variational inequalities (elliptic type) (MSC2000)