A Subgradient Method for Multiobjective Optimization on Riemannian Manifolds

Abstract

In this paper, a subgradient-type method for solving nonsmooth multiobjective optimization problems on Riemannian manifolds is proposed and analyzed. This method extends, to the multicriteria case, the classical subgradient method for real-valued minimization proposed by Ferreira and Oliveira (J. Optim. Theory Appl. 97:93–104, 1998). The sequence generated by the method converges to a Pareto optimal point of the problem, provided that the sectional curvature of the manifold is nonnegative and the multicriteria function is convex.

DOI: 10.1007/s10957-013-0307-7

Cite this paper

@article{Bento2013ASM, title={A Subgradient Method for Multiobjective Optimization on Riemannian Manifolds}, author={Glaydston de Carvalho Bento and Jo{\~a}o X. da Cruz Neto}, journal={J. Optimization Theory and Applications}, year={2013}, volume={159}, pages={125-137} }