A new class of iterative algorithms for approximation-solvability of nonlinear variational inequalities

✍ Scribed by R.U Verma

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 436 KB
• Volume: 41
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/s0898-1221(00)00292-3

✦ Synopsis

Consider the convergence of the projection methods based on a new iterative algorithm for the approximation-solvability of the following class of nonlinear variational inequality (NVI) problems: find an element x* E K such that

where T : K ---, H is a mapping from a nonempty closed convex subset K of a real Hilbert space H into H. The new iterative procedure is characterized as a nonlinear variational inequality (for any arbitrarily chosen initial point x ° E K, and for constants p > 0 and/3 > 0) forall K, andfork O, where (~T(xk) + yk _Xk,X_yk) > O, for all x E K. This nonlinear variational inequality type algorithm has an equivalent projection formula xk+l = pl< [yk--pT(yk)] , where yk = PK [xk --~T (xk ) ] ,

for the projection PK onto g.