One step proximal point schemes for monotone vector field inclusion problems

Abstract

In this paper, we propose one step convex combination of proximal point algorithms for countable collection of monotone vector fields in CAT(0) spaces. We establish Δ-convergence and strong convergence theorems for approximating a common solution of a countable family of monotone vector field inclusion problems. Furthermore, we apply our methods to solve a family of minimization problems, compute Frechét mean and geometric median in CAT(0) spaces, and solve a kinematic problem in robotic motion control. Finally, we give a numerical example to show the efficiency and robustness of the proposed scheme in comparison to a known scheme in the literature.

Keywords

• cat(0) space
• monotone vector field
• proximal point algorithm
• resolvent operator
• tangent space
• δ-convergence