Steepest descent methods for critical points in vector optimization problems

Abstract

In this article, we present steepest descent methods for finding stationary (critical) points of vector optimization problems for maps from an Euclidean space to a Banach space with respect to the partial order induced by a closed, convex and pointed cone with a nonempty interior. Convergence of the generated sequence to a weakly efficient solution of our problem is established under some reasonable additional hypotheses.

Keywords:

• vector optimization
• critical point
• weakly efficient solution
• steepest descent methods
• Banach spaces

AMS Subject Classifications::

• 49J52
• 49M99
• 65K05
• 90C25

Acknowledgements

This work was supported by the Grant NSC 99-2221-E-037-007-MY3 and the National Foundation for Science and Technology Development of Vietnam (NAFOSTED).