Displaying similar documents to “Optimality Conditions for D.C. Vector Optimization Problems under D.C. Constraints”

On localizing global Pareto solutions in a given convex set

Agnieszka Drwalewska, Lesław Gajek (1999)

Applicationes Mathematicae

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Sufficient conditions are given for the global Pareto solution of the multicriterial optimization problem to be in a given convex subset of the domain. In the case of maximizing real valued-functions, the conditions are sufficient and necessary without any convexity type assumptions imposed on the function. In the case of linearly scalarized vector-valued functions the conditions are sufficient and necessary provided that both the function is concave and the scalarization is increasing...

Sufficient Conditions of Optimality for Control Pproblem Governed by Variational Inequalities

Ndoutoume, James (1995)

Serdica Mathematical Journal

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* This work was completed while the author was visiting the University of Limoges. Support from the laboratoire “Analyse non-linéaire et Optimisation” is gratefully acknowledged. The author recently introduced a regularity assumption for derivatives of set-valued mappings, in order to obtain first order necessary conditions of optimality, in some generalized sense, for nondifferentiable control problems governed by variational inequalities. It was noticed that this regularity...

Object library of algorithms for dynamic optimization problems: benchmarking SQP and nonlinear interior point methods

Jacek Błaszczyk, Andrzej Karbowski, Krzysztof Malinowski (2007)

International Journal of Applied Mathematics and Computer Science

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The main purpose of this paper is to describe the design, implementation and possibilities of our object-oriented library of algorithms for dynamic optimization problems. We briefly present library classes for the formulation and manipulation of dynamic optimization problems, and give a general survey of solver classes for unconstrained and constrained optimization. We also demonstrate methods of derivative evaluation that we used, in particular automatic differentiation. Further, we...

Asplund Functions and Projectional Resolutions of the Identity

Zemek, Martin (2000)

Serdica Mathematical Journal

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*Supported by the Grants AV ˇCR 101-97-02, 101-90-03, GA ˇCR 201-98-1449, and by the Grant of the Faculty of Civil Engineering of the Czech Technical University No. 2003. We further develop the theory of the so called Asplund functions, recently introduced and studied by W. K. Tang. Let f be an Asplund function on a Banach space X. We prove that (i) the subspace Y := sp ∂f(X) has a projectional resolution of the identity, and that (ii) if X is weakly Lindel¨of determined,...