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Nonlinear Optimisation with One or Several Objectives: Kuhn–Tucker Conditions

In: Mathematics and Methodology for Economics

Author

Listed:
  • Wolfgang Eichhorn

    (Karlsruhe Institute of Technology (KIT))

  • Winfried Gleißner

    (University of Applied Sciences Landshut)

Abstract

The chapter starts with a discussion of convex sets and functions in $${ \mathbb{R}}^{n}$$ and approximation by quadratic functions. Then it continues with Bellman’s functional equation. For linear regression the method of least squares is used. Next extrema under equality constraints are investigated. We also use envelope theorems and the LeChatelier Principle to determine extrema. The case of inequality constraints is dealt with, too. The chapter ends with an excursion to the Kuhn-Tucker conditions and the optimisation of problems with several objective functions.

Suggested Citation

  • Wolfgang Eichhorn & Winfried Gleißner, 2016. "Nonlinear Optimisation with One or Several Objectives: Kuhn–Tucker Conditions," Springer Texts in Business and Economics, in: Mathematics and Methodology for Economics, edition 1, chapter 8, pages 373-475, Springer.
    • Handle: RePEc:spr:sptchp:978-3-319-23353-6_8
    DOI: 10.1007/978-3-319-23353-6_8
    as

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