Abstract
The aim of this paper is to present a nonconvex duality with a zero gap and its connection with convex duality. Since a convex program can be regarded as a particular case of convex maximization over a convex set, a nonconvex duality can be regarded as a generalization of convex duality. The generalized duality can be obtained on the basis of convex duality and minimax theorems. The duality with a zero gap can be extended to a more general nonconvex problems such as a quasiconvex maximization over a general nonconvex set or a general minimization over the complement of a convex set. Several applications are given.
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On leave from the Institute of Mathematics, Hanoi, Vietnam.
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Thach, P.T. A generalized duality and applications. J Glob Optim 3, 311–324 (1993). https://doi.org/10.1007/BF01096773
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DOI: https://doi.org/10.1007/BF01096773