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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:

49J40 Variational inequalities
49K40 Sensitivity, stability, well-posedness
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
35J85 Unilateral problems; variational inequalities (elliptic type) (MSC2000)

Citations:

Zbl 0886.49004
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