Generalized proximal point algorithms for multiobjective optimization problems

Abstract

In this article, we develop a generalized proximal point algorithm for finding a weak Pareto optimal solution of minimizing an extended vector-valued map with respect to the positive orthant in finite-dimensional spaces by the virtue of a Bregman distance function.

Keywords:

• multiobjective optimization
• generalized proximal point algorithm
• Bregman distance function
• weak Pareto optimal solution

AMS Subject Classifications::

• 90C25
• 90C48
• 90C29
• 65K10
• 49M05

Acknowledgements

This work was partially supported by the Research Committee of The Hong Kong Polytechnic University, the AMSS-PolyU Joint Research Institute for Engineering and Management Mathematics and the Research Grants Council of Hong Kong (PolyU 5317/07E) and the National Natural Science Foundation of China (10831009).