Singularities in Optimization Problems: the Maximum Function

  • Vladimir Igorevich Arnold


Many singularities, bifurcations, and catastrophes (Jumps) arise in all problems in which extrema (maxima and minima) are sought, problems in optimization, control theory and decision theory. For instance, suppose we have to find x such that the value of a function f(x) is maximal (Fig. 46). Under a smooth change of the function the optimal solution changes with a jump from one of the two competing maxima (A) to the other (B).


Normal Form Decision Theory Maximum Function Minimum Function Catastrophe Theory 
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Bibliographical Comments

  1. L. N. Bryzgalova: Singularities of the maximum of a parametrically dependent function. Funkts. Anal. Prilozh. 11:1 (1977), 59–60 (English translation: Funct. Anal. Appl. 11 (1977), 49-51).MathSciNetzbMATHGoogle Scholar
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Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Vladimir Igorevich Arnold
    • 1
  1. 1.Department of MathematicsUniversity of MoscowMoscowUSSR

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