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. © Heldermann Verlag.
|Original language||American English|
|Number of pages||21|
|Journal||Journal of Convex Analysis|
|State||Published - 5 Aug 2009|