One step proximal point schemes for monotone vector field inclusion problems

Abstract

<abstract><p>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 $ \Delta $-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.</p></abstract>