Singularities in Optimization Problems: the Maximum Function

Vladimir I. Arnold
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Vladimir I. Arnold: Steklov Mathematical Institute

Chapter 10 in Catastrophe Theory, 1992, pp 49-52 from Springer

Abstract: Abstract 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. 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).

Keywords: Shock Wave; Decision Theory; Maximum Function; Typical Singularity; Minimum Function (search for similar items in EconPapers)
Date: 1992
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DOI: 10.1007/978-3-642-58124-3_10

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