Hi, Does anyone know the necessary and sufficient conditions for a function to be a DCfunction?
Definition: A function is a DCfunction if and only if it can be written as a differnece of 2 convex functions.
Hi, Does anyone know the necessary and sufficient conditions for a function to be a DCfunction? Definition: A function is a DCfunction if and only if it can be written as a differnece of 2 convex functions. 


For real functions whose domain is a real interval, it is necessary and sufficient that the second derivative is a function of bounded variation on every compact interval in the domain. Or, in terms of distributions, the second derivative must be a measure (a difference of two nonnegative measures). 

