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W 6 _ MU ` Z} u Q x K\ 퉪4 % ސ v ݰ v 3 #~u ~ x K^s T zEc i QE > ` , {c) , ֽ @ tG ނB c xF na?. Hence f is concave Convex functions 3–5 Extendedvalue extension extendedvalue extension f˜of f is f˜(x) = f(x), x ∈ domf, f˜(x) = ∞, x ∈ domf often simplifies notation;. I A F Y Y 3 O X U Z F W O V U P N P D R B E E L N 7 L B A R N W A P 7 V 4 E I K Q V W Y X V Q U A Q V S P W R L Q Q B V Y T V H Q I 6 S V T P H Q A E N X K Z E E M P.

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Minimum element wrt K x is minimum element of S iff for all λ ≻K∗ 0, x is the unique minimizer of λTz over S x S minimal element wrt K • if x minimizes λTz over S for some λ ≻K∗ 0, then x is minimal x1 S x2 λ1 λ2 • if x is a minimal element of a convex set S, then there exists a nonzero λ K∗ 0such that x minimizes. C x g t 擪 @ @ @ ڎ @ @ @ @ @ ڎ @ @.

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