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Math Help - Optimization theory-convex hull help

  1. #1
    Junior Member ginafara's Avatar
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    Optimization theory-convex hull help

    Can someone help me in going about proving the following?

    Let S be any arbitrary set in R^n. Show that conv(S) is the smallest covex set containing S.

    I was thinking a proof by contradiction. But am having a hard time getting it.

    TIA
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  2. #2
    Super Member Rebesques's Avatar
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    Well, if there was a convex superset D of S strictly contained in the convex hull conv(S), then there would be a convex combination of elements of S, contained in D and not contained in conv(S). This contradicts the definition of the convex hull.
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