Displaying similar documents to “On subdifferential calculus and duality in non-convex optimization”

Duality in Constrained DC-Optimization via Toland’s Duality Approach

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.

Characterizations of ɛ-duality gap statements for constrained optimization problems

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.

Strict minimizers of order m in nonsmooth optimization problems

Tadeusz Antczak, Krzysztof Kisiel (2006)

Commentationes Mathematicae Universitatis Carolinae

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In the paper, some sufficient optimality conditions for strict minima of order m in constrained nonlinear mathematical programming problems involving (locally Lipschitz) ( F , ρ ) -convex functions of order m are presented. Furthermore, the concept of strict local minimizer of order m is also used to state various duality results in the sense of Mond-Weir and in the sense of Wolfe for such nondifferentiable optimization problems.