A modified Quasi-Newton method for vector optimization problem

Abstract

In this paper, existence of critical point and weak efficient point of vector optimization problem is studied. A sequence of points in n-dimension is generated using positive definite matrices like Quasi-Newton method. It is proved that accumulation points of this sequence are critical points or weak efficient points under different conditions. An algorithm is provided in this context. This method is free from any kind of priori chosen weighting factors or any other form of a priori ranking or ordering information for objective functions. Also, this method does not depend upon initial point. The algorithm is verified in numerical examples.

Keywords:

• vector optimization
• efficient point
• critical point
• inexact line search
• Quasi-Newton method

AMS Subject Classifications:

• 90C29
• 90C30
• 90C53
• 65K05
• 49M37

Acknowledgements

The authors would like to thank the referees for their detailed comments and suggestions that have significantly improved the content as well as the presentation of the results in the paper.