Subgradient Method for Convex Feasibility on Riemannian Manifolds

Glaydston Bento | Melo, Jefferson

Keywords: Riemannian manifolds; Convex feasibility.

In this paper we present a subgradient type algorithm for solving convex feasibility problem on Riemannian manifold. We prove that the sequence generated by the algorithm converges to a solution of the problem when the sectional curvature of the manifold is non negative. Moreover, assuming a Slater type qualification condition we propose a variant of the first algorithm which ensures finite convergence property, i.e., a feasible point is obtained after a finite number of iteration. We show some examples motivating the application of the algorithm for feasibility problems not necessarily convex (in the usual sense).

Anexos:

• JeffIMPA_preprint.pdf