Projection methods, algorithms, and a new system of nonlinear variational inequalities

✍ Scribed by R.U. Verma

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 433 KB
• Volume: 41
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/s0898-1221(00)00336-9

✦ Synopsis

The convergence of projection methods is based on a new iterative algorithm for the approximation-solvability of the following system of nonlinear variational inequalities (SNVI): determine elements r* , g* E K such that WY!/*) + x* -y*,r-x') 20, for all x E K and for p > 0, and (-rT(x') + y' -x*,x -v*) r 0, for all x E K and for y > 0, where T : K 4 H is a mapping from a nonempty closed convex sub& K of a real Hilbert space H into H. This new class of generalized nonlinear variational inequalities reduces to standard clans of nonlinear variational inequalities, which are widely studied and applied to various problems arising from mathematical sciences, optimization and control theory, and other related fields.