The proximal point method with a vectorial Bregman regularization in multiobjective DC programming

Abstract

For solving constrained multiobjective problems with a vector-valued DC (difference of convex) objective function, we consider a vectorial Bregman regularized proximal point method which extends both the scalar proximal point method for DC functions and the vectorial proximal point method for vector-valued convex functions. By using a vectorial regularization function, our method does not use auxiliary vectorial sequences to make the method a vectorial one but providing an extra flexibility to the method. Some encouraging numerical experiments are presented.

Keywords:

• Proximal point method
• multiobjective optimization
• Bregman distance
• DC function

AMS CLASSIFICATIONS:

• 49M37
• 65K05
• 90C26
• 90C29

Acknowledgments

This work is dedicated to Dr Alfredo Noel Iusem in honor to his 70th birthday.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The first author is supported in part by CNPq grant 424169/2018-5. The research of the second author was supported in part by CNPq grant 305462/2014-8.