Why the svm objective is non convex in first case

to be non convex it’s second derivative must be <0 but it’s not as there is no negative sign so how it’s non convex

For the first objective we try to find values for w and b such that wx+b>0 for positive class and wx+b <0 for negative class, but as in diagram you see L2 and L3 both satisfy this condition but L2 is better funciton. So by this you can infer that, there are many local minimas like L2 and hence the objective is not a convex function.

Hope this cleared your doubt. :blush:

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