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!

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    $\begingroup$ 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! $\endgroup$ Commented Nov 7, 2015 at 7:57

1 Answer 1


You can write the dual SVM objective as maximizing a concave function. Since maximizing is the same thing as minimizing the negative of the objective, and the negative of a concave function is convex, concave maximization and convex minimization are really the same thing; we tend to still use the phrase "convex optimization", because "convex minimization/concave maximization" sounds dumb.


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