Connections among constrained continuous and combinatorial vector optimization

Abstract

In this article, constrained continuous and combinatorial vector optimization problems (VOPs) are considered in the setting of finite-dimensional Euclidean spaces. Equivalence results between constrained integer and continuous VOPs are established by virtue of that between a constrained VOP and its penalized problem. Finally, one of the established equivalences is applied to derive necessary optimality conditions for a constrained integer VOP.

Keywords:

• constrained vector optimization
• penalized vector optimization
• integer vector optimization
• continuous vector optimization
• optimality condition

AMS Subject Classifications::

• 90C27
• 90C10
• 90C33
• 49J40

Acknowledgements

This work is supported by the Research Grants Council of Hong Kong (PolyU 5303/04E), the National Science Foundation of China (10671135, 70831005, 10831009) and Shanghai Pujiang Program. The authors are grateful to one referee, who has provided useful and constructive comments on the early version of this article.