lecture. - CASTLE Lab - Princeton University

Growth Conditions
Definition 6(γ-order growth condition)
Consider a function f and a nonempty set C ⊂ X. Let S ⊂ C be a nonempty
set where f is constant-valued with value fS ∈ R:
f(s) = fS for all s ∈ S.
The γ-order growth condition(γ > 0) holds for f in C if there exists a constant
c > 0 and a neighborhood NS of S such that
f(x)−fS ≥ c[dist(x,S)] γ
for all x ∈ NS C.
Boris Defourny (ORFE) Lecture 6: Perturbation Analysis in Optimization March 15,2012 13 / 26