[筆記] Convex Optimization 2015.11.18

Let {fa:a∈A} be a collection of convex functinos from Rn to R , with same domain, then f(x)=supa∈Afa(x) is a convex function.web Proof1: Take x,y∈domf , θ∈[0,1] , f(θx+(1−θ)y)=≤≤=supafa(θx+(1−θ)y)supa

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