Hölder Continuity of the Saddle Point Set for Real-Valued Functions

ABSTRACT

This paper is concerned with Hölder continuity of the solution to a saddle point problem. Some new sufficient conditions for the uniqueness and Hölder continuity of the solution for a perturbed saddle point problem are established. Applications of the result on Hölder continuity of the solution for perturbed constrained optimization problems are presented under mild conditions. Examples are given to illustrate the obtained results.

KEYWORDS:

• Constrained optimization problems
• Hölder continuity
• linear normed spaces
• saddle points
• strong convexity

MATHEMATICS SUBJECT CLASSIFICATION:

• 46N10
• 90C25
• 90C31
• 90C47

Acknowledgements

The authors express their deep gratitude to the anonymous referees and the associate editor for their valuable comments and suggestions that helped to improve this article. Xiao-Bing Li would like to thank Professor Song Wang for his hospitality during his stay from February 2015 to February 2016 at the School of Mathematics and Statistics of the Curtin University in Perth.