lecture. - CASTLE Lab - Princeton University
lecture. - CASTLE Lab - Princeton University
lecture. - CASTLE Lab - Princeton University
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Perturbation Theorems<br />
Theorem 1 [Bonnans and Shapiro(2000)]<br />
Under the assumptions A1, A2 and B1, the distance between ˜xg and<br />
Sf = argmin Cf satisfy the relation<br />
c[dist(˜xg,Sf)] γ ≤ κdist(˜xg,Sf)+ɛ.<br />
In particular, for the second-order growth condition, the relation yields<br />
dist(˜xg,Sf) ≤ 1<br />
<br />
κ/c + (<br />
2 1<br />
2 κ/c)2 +ɛ/c<br />
≤ κ/c + ɛ/c<br />
For the first-order growth condition, if κ < c, the relation yields<br />
dist(˜xg,Sf) ≤ ɛ/(c −κ).<br />
Boris Defourny (ORFE) Lecture 6: Perturbation Analysis in Optimization March 15,2012 22 / 26
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