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Generalized Lagrange Multiplier Rule

In: Introduction to the Theory of Nonlinear Optimization

Author

Listed:
  • Johannes Jahn

    (Universität Erlangen-Nürnberg, Institut für Angewandte Mathematik)

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.

Suggested Citation

  • Johannes Jahn, 1996. "Generalized Lagrange Multiplier Rule," Springer Books, in: Introduction to the Theory of Nonlinear Optimization, edition 0, chapter 0, pages 109-162, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-03271-8_5
    DOI: 10.1007/978-3-662-03271-8_5
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