Resolvents of convex functions and the shrinking projection method on geodesic spaces (Nonlinear Analysis and Convex Analysis)

Abstract

We apply the shrinking projection method to the convex minimization problems on a complete geodesic space by using the notion of resolvents for convex functions. We consider the calculation errors for metric projections onto the closed convex sets, and obtain the upper bound of the error for the limit of approximation sequence. We also discuss the choice of the coefficient of convex combination used in the iterative process.