Path-based incremental target level algorithm on Riemannian manifolds

ABSTRACT

In this paper, we propose and analyse a path-based incremental target level algorithm for minimizing a constrained convex optimization on complete Riemannian manifolds with lower bounded sectional curvature, where the object function consists of the sum of a large number of component functions. This algorithm extends, to the context of Riemannian manifolds, an incremental subgradient method emplying a version of dynamic stepsize rule. Some convergence results and iteration-complexity bounds of the algorithm are established.

KEYWORDS:

• Path-based incremental target level algorithm
• convex programming
• Riemannian manifolds

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Peng Zhang http://orcid.org/0000-0001-7479-8033

Additional information

Funding

This research was partially supported by the National Natural Science Foundation of China [grant number 11771107].