[筆記] Convex Optimization 2015.10.28

Proposition: Let f:R→R with domf convex and f twice differentiable. Then f is convex if f′′(x)≥0 for all x∈domf . Proof: Let z,x∈domf , then f(z)===≥f(x)+∫zxf′(t)dtf(x)+∫zx(f′(x)+∫txf′′(s)ds)dtf(x)+f′

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