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