Let the Euclidean distance between two points x,y, be denoted by d(x,y):=||x-y||_2.

Given a scalar a>0, can you find a real function f s.t.

a) f>=0, and f(z) = 0 if and only if z = a.

b) f(d(x,y)) is jointly convex in (x,y).

Thanks for your help

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- October 23rd 2012, 08:24 AMnfreris2Convex function of Euclidean distance
Let the Euclidean distance between two points x,y, be denoted by d(x,y):=||x-y||_2.

Given a scalar a>0, can you find a real function f s.t.

a) f>=0, and f(z) = 0 if and only if z = a.

b) f(d(x,y)) is jointly convex in (x,y).

Thanks for your help