Specifically in SVM, it is preferred to have a convex constraint. The preference given to a convex optimization objective is straight-away understandable (to ensure convergence at a global optimum), but it is not quite clear to me why constraints should also be convex.
For eg, in SVM the parameters (weights to the separating hyperplane) are not preferred to be on the surface of a hypersphere. Why?
I read at many places that a non-convex constraint may cause ending up at a local mimima, how is that possible if the objective function is itself convex?
Thank you.
A convex function over a nonconvex domain may have non-global local minima. Just consider to minimize $f(x,y)=x^2 +x +y^2/2$ over the unit circle; you get one non-global minimum.