Erratum to: On convex optimization without convex representation

Abstract

The proof of Theorem 3 in the original publication of the article contains an incorrect statement that we fix below. Theorem 3 Let K in (1.2) be compact and let Assumption 1 hold true. For every fixed μ > 0, choose xμ ∈ K to be an arbitrary stationary point of φμ in K. Then every accumulation point x∗ ∈ K of such a sequence (xμ) ⊂ K with μ → 0, is a global minimizer of f on K, and if ∇ f (x∗) = 0, x∗ is a KKT point of P. Proof Let xμ ∈ K be a stationary point of φμ, which by Lemma 2 is guaranteed to exist. So