lecture. - CASTLE Lab - Princeton University
lecture. - CASTLE Lab - Princeton University
lecture. - CASTLE Lab - Princeton University
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Directionally Differentiable<br />
First- and Second-Order Expansions<br />
A function g(x) is directionally differentiable at x if the directional derivatives<br />
exist for all directions h.<br />
Remark<br />
g ′ (x,h) = lim<br />
t→0 +<br />
g(x +th)−g(x)<br />
t<br />
If g(x) is directional differentiable, we can expand g(x +th) for t > 0 as<br />
g(x +th) = g(x)+tg ′ (x,h)+o(t).<br />
Boris Defourny (ORFE) Lecture 6: Perturbation Analysis in Optimization March 15,2012 17 / 26
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