Generalized weak sharp minima in cone-constrained convex optimization on Hadamard manifolds

Abstract

In this paper, a convex optimization problem with cone constraint (for short, CPC) is introduced and studied on Hadamard manifolds. Some criteria and characterizations for the solution set to be a set of generalized global weak sharp minima, generalized local weak sharp minima and generalized bounded weak sharp minima for (CPC) are derived on Hadamard manifolds.

Keywords:

• Hadamard manifold
• cone-constrained convex programming
• generalized global weak sharp minima
• generalized local weak sharp minima
• generalized bounded weak sharp minima

AMS Subject Classifications:

• 49J50
• 90C48

Acknowledgments

The authors are grateful to the editor and the referees for their valuable comments and suggestions.

Notes

This work was supported by the Key Program of NSFC [grant number 70831005] and the National Natural Science Foundation of China [grant number 11171237].