What is the simplest method to check that a two variable non-liner function is convex or not? Please provide the simplest method.
If you have a closed form, differentiate twice and compute the Hessian (determinant of the matrix of second order partial derivatives). If it is everywhere positive it is convex. Sufficient but not necessary.
Basic functional analysis.
If the functions are differentiablw the condition of positive-definite Hessian matrix is a good condition
Actually it is the criterion that the Hessian (2 x 2 matrix of second derivatives) has non-negative eigenvalues everywhere. (They do NOT need to be positive.)
if a hessian matrix is 3X3 and its 1st order principal minors are 0, positive and negative respectively;
2nd order principal minors are negative, 0 and negative respectively;
and 3rd order principal minor is positive.
Then what can i conclude about this function, is it convex or, quasi-convex or, non-convex function.
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