Partially relaxed cocoercive variational inequalities and auxiliary problem principle

[摘要] LetT:K→Hbe a mapping from a nonempty closed convex subsetKof a finite-dimensional Hilbert spaceHintoH. Letf:K→ℝbe proper, convex, and lower semicontinuous onKand leth:K→ℝbe continuously Frećhet-differentiable onKwithh′(gradient ofh),α-strongly monotone, andβ-Lipschitz continuous onK. Then the sequence{xk}generated by the general auxiliary problem principle converges to a solutionx*of the variational inequality problem (VIP) described as follows: find an elementx*∈Ksuch that〈T(x*),x−x*〉+f(x)−f(x*)≥0for allx∈K.

[学科分类] 应用数学