Preprint D102/2013
A Steepest Descent-like Method for Variable Order Vector Optimization Problems

G. Bouza Allende | Bello Cruz, J.Y.

**Keywords: **
K-convexity · variable order · vector optimization · weakly efficient points

In some applications, the comparison between two elements may depend on the point leading to the so called variable order structure. Optimality concepts may be extended to this more general framework. In this paper, we extend the steepest descent-like method for smooth unconstrained vector optimization problem under a variable ordering structure. Roughly speaking, we obtain that every accumulation point of the generated sequence satisfies a necessary first order condition. We discuss the consequence of this fact in the convex case.