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.
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© 2011 Springer-Verlag Berlin Heidelberg
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Jahn, J. (2011). Generalized Lagrange Multiplier Rule. In: Vector Optimization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17005-8_7
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DOI: https://doi.org/10.1007/978-3-642-17005-8_7
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-17004-1
Online ISBN: 978-3-642-17005-8
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