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Mathematische Operationsforschung und Statistik Series Optimization
Article . 1983 . Peer-reviewed
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Differentiable Programming in Banach Spaces

Differentiable programming in Banach spaces
descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1983 English Publisher:Informa UK LimitedJournal:Mathematische Operationsforschung und Statistik. Series Optimization, volume 14, pages 499-508 (issn: 0323-3898, Copyright policy )
Authors: B.M. Glover;

doi: 10.1080/02331938308842884

Differentiable Programming in Banach Spaces

Abstract

For a differentiable mathematical program defined in a Banach space, generalized Kuhn-Tucker necessary conditions are obtained for optimality. A closed-cone hypothesis is replaced by a closed-range condition on a linear operator, the latter being automatic when the constraints have finite dimensional range. Asymptotic conditions are avoided, by expanding the cone containing the Lagrange multiplier. Generalizations are given also of the Farkas and Motzkin theorems.

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Keywords

Programming in abstract spaces, Banach space, Numerical methods based on nonlinear programming, Nonlinear programming, closed-cone hypothesis, generalized Kuhn- Tucker necessary conditions, Lagrange multiplier, Optimality conditions for problems in abstract spaces, differentiable mathematical program, closed-range condition

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
4
Average
Top 10%
Average
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