Some characterizations of a nonlinear scalarizing function via oriented distance function

Abstract

This paper aims at investigating some properties concerned with a nonlinear scalarizing function via oriented distance function. The convexity, continuity and Lipschitz continuity of the nonlinear scalarizing function are showed under some suitable conditions. As an application, we establish Lipschitz continuity of strongly approximate solution mapping for l-type order relation to parametric set optimization problems by using convexity and Lipschitz continuity of the nonlinear scalarizing function.

Keywords:

• Nonlinear scalarizing function
• oriented distance function
• convexity
• continuity
• Lipschitz continuity

AMS Subject Classifications:

• 49J45
• 49J53
• 90C29
• 90C31

Acknowledgments

The author is grateful to the two anonymous reviewers whose helpful comments and suggestions have led to much improvement of the paper.

Disclosure statement

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

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (11801257).