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.
['Dmitriy Drusvyatskiy', 'Alexander Ioffe']
Quadratic growth and critical point stability of semi-algebraic functions