Generalized Lagrange Multiplier Rule

Johannes Jahn ()
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Johannes Jahn: Universität Erlangen-Nürnberg

Chapter Chapter 7 in Vector Optimization, 2011, pp 161-188 from Springer

Abstract: Abstract In this chapter we present a generalization of the famous and wellknown Lagrange multiplier rule published in 1797. Originally, Lagrange formulated his rule for the optimization of a real-valued function under side-conditions in the form of equalities. In this context we investigate an abstract optimization problem with equality and inequality constraints. For this problem we derivea generalized multiplier rule as a necessary optimality condition and we show under which assumptions this multiplier rule is also sufficient for optimality. The results are also applied to multiobjective optimization problems.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-17005-8_7

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DOI: 10.1007/978-3-642-17005-8_7

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