Abstract:

In this paper we present two inexact proximal point algorithms to solve
minimization problems for quasiconvex objective functions on Hadamard manifolds.
We prove that under natural assumptions the sequence generated by the algorithms
are well defined and converge to critical points of the problem. We also present an
application of the method to demand theory in economy.

Key words: Proximal point method ·, Quasiconvex function ·, Hadamard manifolds ·
Nonsmooth optimization ·, Abstract subdifferential