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Norm-Cone Conjugation for Nonconvex Optimization: Scalar Duality and Exact Distance Penalization
We develop a norm-cone conjugation framework, generated by translated norm-cones \[ x\mapsto r-α\|x-x_0\|, \qquad α\geq 0. \] We show that this family generates the same abstract-convex class as the family of Lipschitz continuous concave functions, and exploit its explicit metric structure to obtain
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