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Lagrangian duality for nonconvex optimization problems with abstract convex functions (2011.09194v1)
Published 18 Nov 2020 in math.OC
Abstract: We investigate Lagrangian duality for nonconvex optimization problems. To this aim we use the $\Phi$-convexity theory and minimax theorem for $\Phi$-convex functions. We provide conditions for zero duality gap and strong duality. Among the classes of functions, to which our duality results can be applied, are prox-bounded functions, DC functions, weakly convex functions and paraconvex functions.