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In this paper, we study some non-traditional schemes of proximal point algorithm for nonsmooth convex functionals in a Banach space. The proximal approximations to their minimal points and/or their minimal values are considered separately for unconstrained and constrained minimization problems on convex closed sets. For the latter we use proximal point algorithms with the metric projection operators...
In this work, we study the following Generalized Variational Inequality Problem (for short, GVIP): Given a closed convex set K in a reflexive Banach space E with the dual E∗, a multifunction T:K→2E∗, and a vector b∈E∗, find x̄∈K such that there exists ū∈T(x̄) satisfying 〈ū−b,y−x̄〉≥0,for all y∈K. By using generalized projection and the well-known Fan–KKM Theorem, we prove existence results for solutions...
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