Optimality conditions and Toland's duality for a nonconvex minimization problem.
Laghdir, M. (2003)
Matematichki Vesnik
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Displaying similar documents to “On subdifferential calculus and duality in non-convex optimization”
Optimality conditions and Toland's duality for a nonconvex minimization problem.
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.
A general separation theorem for mappings, saddle-points duality and conjugate functions
M. Altman (1970)
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Jiří V. Outrata, Jiří Jarušek (1984)
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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 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 in constrained nonlinear mathematical programming problems involving (locally Lipschitz) -convex functions of order are presented. Furthermore, the concept of strict local minimizer of order 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.