Maximizing (20) delivers the same solution as maximizing (6). The limit of
—к , . ч _ . . ... .
L (x*) for к → ∞ exists and is given by:
Iim Lk(x*r) = pi
k→∞ .
i∈ ^max
Next, consider L(x* + d) with d ∈ Rn and ∣∣d∣∣ = δ, δ sufficiently small. From
lemma 4 and (20) it follows that
_k r ek(b(≈i.sι)+ε)
L (xr + d) > gkL(^*,s1) Pmin
where pm∙in = mini Pi. Therefore, there exists a к < ∞ such that for all к > к
Lk(xtr + d) >Lk(x*)
__ . . . _ — к . . . . . „ — к , ч
From the strict convexity of L (∙) it follows that the minimum xk of L (∙) must
be within distance δ from xtr for all к > к, which establishes the claim.
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___, ___, G.A. Tirmuhambetova, and N. Williams, “Robustness and
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