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Introduction

  • Hubertus Th. Jongen
  • Peter Jonker
  • Frank Twilt
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 47)

Abstract

Let ℝ n be the n-dimensional Euclidean space with the usual inner product 〈·, ·〉, 〈x, y〉 = x y, and norm \(\left\| x \right\| = \sqrt {\left\langle {x,x} \right\rangle } \). Let M ⊂ ℝ n , M ≠ ∅ and f : M → ℝ a function. An \(\bar x \in M\) M having the property: \(f\left( {\bar x} \right)f(x)\) holds for all xM, is called a global minimum for f . If \(f\left( {\bar x} \right) \leqslant f(x)\) holds for all xMO, O being a ℝ n -neighborhood of \(\bar x\), then \(\bar x\) is called a local minimum for f. Obviously, a global minimum is also a local minimum. Local (global) maxima of f are defined to be local (global) minima for the function -f.

Keywords

Local Minimum Saddle Point Local Maximum Global Minimum Planar Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • Hubertus Th. Jongen
    • 1
  • Peter Jonker
    • 2
  • Frank Twilt
    • 2
  1. 1.Department of MathematicsAachen University of TechnologyAachenGermany
  2. 2.Department of Mathematical SciencesUniversity of TwenteEnschedeThe Netherlands

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