# Support Vector Machine Optimization Convexity

The SVM derivation is centered on convex optimization. By definition, convex optimization requires a convex objective function and convex or linear constraints. The task is to minimize this function.

My question is: When the SVM problem is converted from primal to dual, it becomes a maximization problem (in the dual form). Since we are no longer minimizing a convex function, does this still qualify to be called convex optimization? I know this will be a silly question to an expert in this field – but I have to put on a brave face to ask it!

• I don't think this is a silly question as it shows you understand what's going on pretty well and aren't afraid to question vague elements. Keep it up! – Marc Claesen Nov 7 '15 at 7:57