Trust region methods for solving multiobjective optimisation

Abstract

This paper first proposes a trust region algorithm to obtain a stationary point of unconstrained multiobjective optimisation problem. Under suitable assumptions, the global convergence of the new algorithm is established. We then extend the trust region method to solve the non-smooth multiobjective optimisation problem.

Keywords:

• trust region methods
• multiobjective optimisation
• stationary point
• convergence
• Pareto optimisation

AMS Subject Classification:

• 90C29
• 90C30

Acknowledgements

We are grateful to the editors and the two anonymous referees for their careful reading of the manuscript and their helpful suggestions. This work was supported by the National Science Foundation Grant of China (No. 10926077). This work was supported by Natural Scientific Research Innovation Foundation in Harbin Institute of Technology (No. HIT.NSRIF.2009074) and program of excellent Team in Harbin Institute of Technology. This work was supported by both China Post-doctoral Science Foundation (No. 01107172) and Heilongjiang Province Post-doctoral Science Foundation (No. 01106961).