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Numerical Solution of Systems of Nonlinear Inequalities

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Optimization and Operations Research

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 117))

Abstract

In many cases we are concerned with the problem of solving a system of nonlinear inequalities, for example, if we have to construct a feasible initial point for an algorithm solving

$$\min \varphi (x)$$
$$x:{{f}_{i}}(x)\le 0,i=,...,m ,$$

that is a point x0∈ℝn with fi(xo) ≤ 0, i=1,…,m. Therefore, we will study now the following problem:

(1.1)Problem: Let f:ℝn → ℝm be continuously (Fréchet) differentiable.

Find x∈ℝn such that

$$f(x)\le 0$$

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Author information

Authors and Affiliations

  1. Institut für Angewandte Mathematik, Universität Würzburg, 87 Würzburg Am Hubland, Germany

    Klaus Schittkowski

Authors
  1. Klaus Schittkowski
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Editor information

Editors and Affiliations

  1. Fakultät für Mathematik und Informatik, Universität Mannheim, Schloß, 6800, Mannheim 1, Deutschland

    Werner Oettli

  2. Mathematisches Institut A, Universität Stuttgart, 7000, Pfaffenwaldring 57, Stuttgart 80, Deutschland

    Klaus Ritter

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© 1976 Springer-Verlag Berlin · Heidelberg

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Schittkowski, K. (1976). Numerical Solution of Systems of Nonlinear Inequalities. In: Oettli, W., Ritter, K. (eds) Optimization and Operations Research. Lecture Notes in Economics and Mathematical Systems, vol 117. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46329-7_23

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  • DOI: https://doi.org/10.1007/978-3-642-46329-7_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07616-2

  • Online ISBN: 978-3-642-46329-7

  • eBook Packages: Springer Book Archive

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