lecture. - CASTLE Lab - Princeton University

Example 1
Hölder and Lipschitz Continuity for Functions
f0(x) = ax α with α ∈ (0,1] and α ∈ R satisfies |f0(x)−f0(y)| ≤ |a||x −y| α on
C = [0,u].
Example 2
Let f be a continuous function differentiable on an open set S, with gradient
∇f(x) on S. Let C be a compact convex subset of S. Then f is Lipschitz
continuous on C modulus c = maxx∈C∇xf(x).
Boris Defourny (ORFE) Lecture 6: Perturbation Analysis in Optimization March 15,2012 10 / 26