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

Wolfgang Eichhorn and Winfried Gleißner
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Wolfgang Eichhorn: Karlsruhe Institute of Technology (KIT)
Winfried Gleißner: University of Applied Sciences Landshut

Chapter 8 in Mathematics and Methodology for Economics, 2016, pp 373-475 from Springer

Abstract: 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.

Keywords: Objective Function; Saddle Point; Capital Stock; Hessian Matrix; Lagrange Function (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/978-3-319-23353-6_8

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