New concepts in nondifferentiable programming
J-B. Hiriart-Urruty (1979)
Mémoires de la Société Mathématique de France
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J-B. Hiriart-Urruty (1979)
Mémoires de la Société Mathématique de France
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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.
Jiří V. Outrata, Jiří Jarušek (1984)
Kybernetika
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A. L. Brown, H. L. Vasudeva
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The paper is concerned with the Fréchet differentiability and operator convexity of the operator functions on sets of self-adjoint operators on finite-dimensional inner product spaces which are associated with real-valued functions of one or two variables. In Part I it is shown that if a real-valued function is L times continuously differentiable then the associated operator functions are L times Fréchet differentiable with continuous Fréchet derivatives. It is shown that the operator...
Chen, Jung-Chih, Lai, Hang-Chin (2002)
Applied Mathematics E-Notes [electronic only]
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Papageorgiou, Nikolaos S., Papageorgiou, Apostolos S. (1992)
International Journal of Mathematics and Mathematical Sciences
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Laghdir, M. (2003)
Matematichki Vesnik
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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.