Proximal Point Algorithm for Quasi-Convex Minimization Problems in Metric Spaces. (12th March 2018) - Khatibzadeh, Hadi; Mohebbi, Vahid
ABSTRACT: In this paper, the proximal point algorithm for quasi-convex minimization problem in nonpositive curvature metric spaces is studied. We prove Δ -convergence of the generated sequence to a critical point (which is defined in the text) of an objective quasi-convex, proper and lower semicontinuous function with at least a minimum point as well as some strong convergence results to a minimum point with some additional conditions. The results extend the recent results of the proximal point algorithm in Hadamard manifolds and CAT(0) spaces.