Hi all, I have a few questions regarding DC programming:
I appreciate the insight, Sina 
I think you have misunderstood "difference of convex" programming. Boyd's lecture slides state the problem as: minimize \( f_0 (x)  g_0 (x) \) subject to \( f_i (x)  g_i (x) \le 0 \) for \( i=1,\dots, m\) where \( f_i\) and \( g_i \) are given convex functions. The symbol \( x \) refers to a (vector of) variable(s), not a constant. answered 10 Jul '13, 23:25 Austin Buchanan Thanks for the clarification, you are right. Do you have any thoughts on my first two questions? i.e., if I did have a DC problem, what would be a good tool to solve it with?
(12 Jul '13, 12:00)
Sina
BARON (http://archimedes.cheme.cmu.edu/?q=baron) is a generalpurpose solver. I know very little about DC problems.
(12 Jul '13, 13:24)
Austin Buchanan
Thanks a lot. I just reformulated the problem, and I think the variable in my problem is the function f which belongs to a class of functions F. (FYI, this problem is known as the maximum discrepancy of F, see page 2 in http://machinelearning.wustl.edu/mlpapers/paper_files/BartlettM02.pdf )
(14 Jul '13, 14:44)
Sina

Did you mean \(\max_g\) in the second term? Are your variables the functions \(f\) and \(g\) and, if so, are there any restrictions on them besides being convex?
Sorry there was a typo. I just fixed it. So in the 3rd part of my question, there is no "g". In this particular example, there are two convex functions: one is \(\sum_i L(f(x_i))\) and one is \(\sum_j L(f(y_j))\).
Convex functions of what? You said the x and y symbols were constants.
Yes, f is convex over the set of real numbers. So I am trying to see if this optimization is solvable for any given set of x_i and y_i constants if f is allowed to iterate over a class functions as long as it is a convex function.
Why are there two 'max' terms?