Generalized solutions to interval linear programmes and related necessary and sufficient optimality conditions

Abstract

Recently, some new concepts of optimal solution to interval linear program are introduced which include some existing concepts of optimal solution as special cases. This paper considers generalized optimal solution to interval linear programming problems. The new concepts of optimal solution are introduced in a more general and unified framework. Most existing optimal solution concepts of interval linear program in the literature are special cases in this framework. Necessary and sufficient conditions for checking three kinds of these newly defined optimal solutions are developed.

Keywords:

• interval linear system
• interval linear programming
• optimal solution
• tangent cone

Mathematics Subject Classification (2010):

• 65G40

Acknowledgements

We thank anonymous referees for their constructive comments and suggestions that helped to improve the paper. The results in Lemmas 2.4, 4.2 and Theorem 4.2 are enhanced by the suggestion from one of the reviewers.

Funding

This project is partially supported by the NSF of Zhejiang Province [grant number LY14A010028] and NNSF of China [grant numbers 71471051, 11171316].