User:Jarle Pahr/Convexity

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Notes on convexity as applied to optimization:

How to determine if a function is convex/concave:

A function is convex iff its [epigrah] is a convex set.

If f is a multivaried function on a convex open set S, with continous partial derivatives, then:

  • f is concave iff H(x) is negative semi-definite for all x in S.
  • f is convex iff H(x) is positive semi-definite for all x in S.