Abstract
In this chapter we investigate optimization problems with constraints in the form of inequalities and equalities. For such constrained problems we formulate a multiplier rule as a necessary optimality condition and we give assumptions under which this multiplier rule is also a sufficient optimality condition. The optimality condition presented generalizes the known multiplier rule published by Lagrange in 1797. With the aid of this optimality condition we deduce then the Pontryagin maximum principle known from control theory.
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© 1994 Springer-Verlag Berlin Heidelberg
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Jahn, J. (1994). Generalized Lagrange Multiplier Rule. In: Introduction to the Theory of Nonlinear Optimization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-02985-5_5
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DOI: https://doi.org/10.1007/978-3-662-02985-5_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-02987-9
Online ISBN: 978-3-662-02985-5
eBook Packages: Springer Book Archive