Quadratic growth and critical point stability of semi-algebraic functions

D. Drusvyatskiy, A. D. Ioffe

Published 2013-09-05, updated 2014-12-20Version 2

We show that quadratic growth of a semi-algebraic function is equivalent to strong metric subregularity of the subdifferential --- a kind of stability of generalized critical points. In contrast, this equivalence can easily fail outside of the semi-algebraic setting. As a consequence, we derive necessary conditions and sufficient conditions for optimality in subdifferential terms.