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Zbl 0889.49006
Noor, Muhammad Aslam
Some recent advances in variational inequalities. II: Other concepts. (English)
[J] N. Z. J. Math. 26, No.2, 229-255 (1997). ISSN 1171-6096/e

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.
[P.Neittaanmäki (Jyväskylä)]

MSC 2000:: *49J40 Variational methods including variational inequalities
49K40 Sensitivity of optimal solutions in the presence of perturbations
90C33 Complementarity problems
35J85 Unilateral problems; variational inequalities (elliptic type)

Keywords: variational inequalities; Wiener-Hopf equations; projection algorithm; auxiliary principle; invex; preinvex; variational-like inequalities; parallel algorithms; complementarity problems

Citations: Zbl 0886.49004

Cited in: Zbl 1139.49012 Zbl 0988.49003

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