A new nonlinear scalarization function and applications

Abstract

In this paper, a new nonlinear scalarization function, which is a generalization of the oriented distance function, is introduced. Some properties of the function are discussed. Then the function is applied to obtain some new optimality conditions and scalar representations for set-valued vector optimization problems with set optimization criteria. In terms of the function and the image space analysis, some new alternative results for generalized parametric systems are derived.

Keywords:

• nonlinear scalarization function
• set optimization
• generalized parametric system
• image space analysis
• optimality condition

AMS Subject Classifications:

• 49K05
• 90C29

Acknowledgements

The authors thank the two anonymous reviewers for their valuable comments and suggestions, which helped to improve the paper.

Conflict of interest disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This research was supported by the National Natural Science Foundation of China [grant number 11171362], [grant number 11426055]; Specialized Research Fund for the Doctoral Program of Higher Education [grant number 20120191110031]; Basic and Advanced Research Project of CQ CSTC [grant number cstc2014jcyjA00044]; and the Doctor Start-up Foundation of University of Posts and Telecommunications [grant numbers A2014-15, A2014-16].