A Steepest Descent-Like Method for Variable Order Vector Optimization Problems - Bello Cruz, J. Y.; Bouza Allende, G. (Journal of optimization theory and applications, 2014)
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 problems under a variable order structure. Roughly speaking, we see 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.