On programming when the positive cone has an empty interior

descriptionPublicationkeyboard_double_arrow_right Article 01 Nov 1990 English Publisher:Springer Science and Business Media LLCJournal:Journal of Optimization Theory and Applications, volume 67, pages 395-410 (issn: 0022-3239, eissn: 1573-2878,

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Authors: De Araujo, A. P.; Monteiro, P. K.;

doi: 10.1007/bf00940482

On programming when the positive cone has an empty interior

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Abstract

We present a condition which is equivalent to the existence of the Lagrange multiplier for the general convex programming problem. This condition enables one to study a hypothesis distinct from the one of nonempty interior of the positive cone of the space of restrictions, that is commonly used. Simple examples of this condition are given. We also explore the relationship of this condition with the subdifferentiability of the primal functional.

Related Organizations

Federal University of Rio de Janeiro
Brazil
Instituto Nacional de Matemática Pura e Aplicada
Brazil

Keywords

Convex programming, subdifferentiability, Nonsmooth analysis, Lagrange multiplier, positive cones

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