Proximal point methods for quasiconvex and convex functions with Bregman distances on Hadamard manifolds. (English) Zbl 1176.90361
Summary: This paper generalizes the proximal point method using Bregman distances to solve convex and quasiconvex optimization problems on Hadamard manifolds. We will proved that the sequence generated by our method is well defined and converges to an optimal solution of the problem. Also, we obtain the same convergence properties for the classical proximal method, applied to quasiconvex problems. Finally, we give some examples of Bregman distances in non-Euclidean spaces.
MSC:
90C25 | Convex programming |
49M30 | Other numerical methods in calculus of variations (MSC2010) |