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Some recent advances in variational inequalities. II: Other concepts. (English) Zbl 0889.49006
This paper continues a previous work of the author [N. Z. J. Math. 26, No. 1, 53-80 (1997; Zbl 0886.49004)]. It is devoted to variational inequalities in Hilbert spaces corresponding to closed convex subsets, i.e., to indicator functions. The first two sections concern “fuzzy variational inequalities” and “random variational inequalities”. As usual, an equivalent “fuzzy” (or “random”) Wiener-Hopf equation is associated and some algorithms of fixed point type are defined and their convergence is briefly discussed. In the next section, on “sensitivity analysis”, some continuity properties with respect to the parameters are proved, without differentiability results. The last three parts are devoted to numerical results, more algorithms and conclusions. There is one example for a third order ordinary differential equation of a simple nature. However, this is quite unclear since the fixed convex subset yields four boundary conditions and, in general, no solution is possible.

MSC:
49J40Variational methods including variational inequalities
49K40Sensitivity, stability, well-posedness of optimal solutions
90C33Complementarity and equilibrium problems; variational inequalities (finite dimensions)
35J85Unilateral problems; variational inequalities (elliptic type) (MSC2000)