Notes on convexity as applied to optimization:
How to determine if a function is convex/concave: http://www.economics.utoronto.ca/osborne/MathTutorial/CVNF.HTM
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.