Characterization of quadratic growth of extended-real-valued functions

Abstract

Abstract This paper shows that the sharpest possible bound in the second-order growth condition of a proper lower semicontinuous function can be attained under some assumptions. We also establish a relationship among strong metric subregularity, quadratic growth, the positive-definiteness property of the second-order subdifferential/generalized Hessian, the strong metric regularity, and tilt stability in a finite-dimensional setting.

Keywords

• quadratic growth
• Mordukhovich (limiting) subdifferential
• strong metric regularity
• strong metric subregularity
• prox-regular