Supplement

We provide the proof (Section A) of our main result presented in Section 3. Section B is about an additional numerical illustration in the context of kernel ridge regression on the importance of hard shape constraints in case of increasing level of noise. 'above' the affine hyperplane defined by normal vector Our results are summarized in Figure 1(b). To illustrate the tightening property of Theorem 3, i.e. that (n 1) (n 1) By construction both measures are zero for SOC. ( d 2)