A Steepest Descent-Like Method for Variable Order Vector Optimization Problems
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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.
KeywordsConvexity Gradient-like method Variable order Vector optimization Weakly efficient points
The authors would like to thank the anonymous referees, whose suggestions helped us to improve the presentation of this paper. We also very grateful to Prof. Dr. Ole Peter Smith for correcting the manuscript.
This research was supported by Project CAPES-MES-CUBA 226/2012 “Modelos de Otimização e Aplicações”. First author was partially supported by PROCAD-nf-UFG/UnB/IMPA research and PRONEX-CNPq-FAPERJ Optimization research.
- 21.Luc, D.T.: Theory of Vector Optimization. Lecture Notes in Economics and Mathematical Systems, vol. 319. Springer, Berlin (1989) Google Scholar
- 23.Luc, D.T.: Pareto Optimality, Game Theory and Equilibria. In: Pareto Optimality. Springer Optimization and its Applications, vol. 17, pp. 481–515 (2008) Google Scholar
- 27.Peressini, A.L.: Ordered Topological Vector Space. Harper and Row, New York (1967) Google Scholar