More than first-order developments of convex functions: primal-dual relations.
Lemaréchal, C., Sagastizábel, C. (1996)
Journal of Convex Analysis
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Lemaréchal, C., Sagastizábel, C. (1996)
Journal of Convex Analysis
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Laghdir, M., Benkenza, N. (2003)
Serdica Mathematical Journal
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2000 Mathematics Subject Classification: 90C48, 49N15, 90C25 In this paper we reconsider a nonconvex duality theory established by B. Lemaire and M. Volle (see [4]), related to a primal problem of minimizing the difference of two convex functions subject to a DC-constraint. The purpose of this note is to present a new method based on Toland-Singer duality principle. Applications to the case when the constraints are vector-valued are provided.
Tran Quoc Chien (1992)
Kybernetika
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Horaţiu-Vasile Boncea, Sorin-Mihai Grad (2013)
Open Mathematics
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In this paper we present different regularity conditions that equivalently characterize various ɛ-duality gap statements (with ɛ ≥ 0) for constrained optimization problems and their Lagrange and Fenchel-Lagrange duals in separated locally convex spaces, respectively. These regularity conditions are formulated by using epigraphs and ɛ-subdifferentials. When ɛ = 0 we rediscover recent results on stable strong and total duality and zero duality gap from the literature.