A General Duality Scheme for Nonconvex Minimization Problems with a Strict Inequality Constraint

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We establish a duality formula for the problem Minimize ƒ(x)+g(x) for h(x)+k(x)<0 where g, k are extended-real-valued convex functions and f, h belong to the class of functions that can be written as the lower envelope of an arbitrary family of convex functions. Applications in d.c. and Lipschitzian optimization are given.

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