Monotonicity of fixed point and normal mappings associated with variational inequality and its application. (English) Zbl 1010.90084

Zhao, Yun-Bin; Li, Duan

SIAM J. Optim. 11, No. 4, 962-973 (2001).

Summary: We prove sufficient conditions for the monotonicity and the strong monotonicity of fixed point and normal maps associated with variational inequality problems over a general closed convex set. Sufficient conditions for the strong monotonicity of their perturbed versions are also shown. These results include some well known in the literature as particular instances. Inspired by these results, we propose a modified Solodov and Svaiter iterative algorithm for the variational inequality problem whose fixed point map or normal map is monotone.

MSC:

90C33	Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
58E35	Variational inequalities (global problems) in infinite-dimensional spaces

Keywords:

variational inequalities; cocoercive maps; (strongly) monotone maps; fixed point and normal maps; iterative algorithm