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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
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
Download citation
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