Norm-preserving extension of convex Lipschitz functions

By Stefan Cobzas, C. Mustăța. 1978

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Differentially Private Empirical Risk Minimization: Efficient Algorithms and Tight Error Bounds (2014, background): “The following lemma (which is a variant of Theorem 1 in [13]) asserts that any convex Lipschitz efficiently computable function defined”
Private Empirical Risk Minimization, Revisited (2014, background): “The following lemma (which is a variant of Theorem 1 in [9]) asserts that any convex Lipschitz efficiently computable function defined over some convex set C has a Lipschitz extension (with the same Lipschitz constant) over Rp that is also convex and efficiently computable where the computation effi”