Metric regularity of a positive order for generalized equations

Abstract

This paper focuses on the metric regularity of a positive order for generalized equations. More concretely, we establish verifiable sufficient conditions for a generalized equation to achieve the metric regularity of a positive order at its a given solution. The provided conditions are expressed in terms of the Fréchet coderivative/or the Mordukhovich coderivative/or the Clarke one of the corresponding multifunction formulated the generalized equation. In addition, we show that such sufficient conditions turn out to be also necessary for the metric regularity of a positive order of the generalized equation in the case where the multifunction established the generalized equation is closed and convex.

Keywords:

• metric q-regularity
• sufficient condition
• multifunction
• coderivative

AMS Subject Classifications:

• 46T20
• 49J53
• 49J52
• 90C29
• 90C31

Acknowledgements

The author would like to thank the editor and the referees for their helpful comments and suggestions.

Additional information

Funding

This research was funded by Vietnam National Foundation for Science and Technology (NAFOSTED).