Error bound and well-posedness with respect to an admissible function

Abstract

Using techniques of variational analysis and in terms of subdifferential, we study the generalized error bound defined by an admissible function, an interesting extension of the Hölder error bound and the usual error bound. With the help of a chain rule of subdifferential established in the paper, without the solvability assumption, we provide a sufficient condition for a nonconvex inequality to have a global generalized error bound. We also provide some sufficient and/or necessary conditions for an inequality to have Hölder error bounds. As applications, we consider well-posedness with respect to an admissible function.

Keywords:

• Hölder error bound
• well-posedness
• subdifferential

AMS Subject Classifications:

• 90C31
• 49K40
• 49J52

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This author was supported by the National Natural Science Foundation of P. R. China [grant number 11371312] and IRTSTY.