Generalized Lagrange Multiplier Rule

Johannes Jahn
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Johannes Jahn: Universität Erlangen-Nürnberg, Institut für Angewandte Mathematik

Chapter Chapter 5 in Introduction to the Theory of Nonlinear Optimization, 1996, pp 109-162 from Springer

Abstract: 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.

Keywords: Optimal Control Problem; Minimal Point; Directional Derivative; Regularity Assumption; Pontryagin Maximum Principle (search for similar items in EconPapers)
Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-662-03271-8_5

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DOI: 10.1007/978-3-662-03271-8_5

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