Displaying similar documents to “On relations among the generalized second-order directional derivatives”

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.

The calculus of operator functions and operator convexity

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...

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.

On necessary optimality conditions in a class of optimization problems

Jiří V. Outrata (1989)

Aplikace matematiky

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In the paper necessary optimality conditions are derived for the minimization of a locally Lipschitz objective with respect to the consttraints x ∈ S , 0 ∈ F ( x ) , where S is a closed set and F is a set-valued map. No convexity requirements are imposed on F . The conditions are applied to a generalized mathematical programming problem and to an abstract finite-dimensional optimal control problem.