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2015 | OriginalPaper | Buchkapitel

2. Duality for Scalar Optimization Problems

verfasst von : Sorin-Mihai Grad

Erschienen in: Vector Optimization and Monotone Operators via Convex Duality

Verlag: Springer International Publishing

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Abstract

Assigning a dual problem to a given minimization problem provides, due to the weak duality, a lower bound for the objective values of the latter. Moreover, if strong duality can be proven, the optimal objective values of the two problems coincide and they can be determined since usually the dual problem has a simpler structure than the primal one and can be easier solved. Moreover, necessary and sufficient optimality conditions for the primal-dual pair of problems in discussion can be derived and these can be employed for determining the optimal solutions of the primal problem when the ones of the dual, guaranteed by the strong duality statement, were already identified.

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Vorheriges Kapitel Introduction and Preliminaries

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Titel: Duality for Scalar Optimization Problems
verfasst von: Sorin-Mihai Grad
Verlag: Springer International Publishing
Buch: Vector Optimization and Monotone Operators via Convex Duality
Print ISBN: 978-3-319-08899-0

Electronic ISBN: 978-3-319-08900-3

Copyright-Jahr: 2015
DOI: https://doi.org/10.1007/978-3-319-08900-3_2