Monotonicity of Fixed Point and Normal Mappings Associated with Variational Inequality and Its Application
Yun-Bin Zhao, Duan Li · SIAM Journal on Optimization · 2001
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.