A natural extension of the classical envelope theorem in vector differential programming

F. García Castaño () and M. Melguizo Padial ()

Journal of Global Optimization, 2015, vol. 63, issue 4, 757-775

Abstract: The aim of this paper is to extend the classical envelope theorem from scalar to vector differential programming. The obtained result allows us to measure the quantitative behaviour of a certain set of optimal values (not necessarily a singleton) characterized to become minimum when the objective function is composed with a positive function, according to changes of any of the parameters which appear in the constraints. We show that the sensitivity of the program depends on a Lagrange multiplier and its sensitivity. Copyright Springer Science+Business Media New York 2015

Keywords: Envelope theorem; Set-valued map; Tangential regularity; Contingent or bouligand derivative; Clarke derivative (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10898-015-0307-2

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