Book ChapterDOI
Singularities in Optimization Problems: the Maximum Function
Vladimir I. Arnold
- pp 43-46
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Many singularities, bifurcations, and catastrophes (jumps) arise in all maxima and minima problems ; such problem arise, for instance, in optimization, control theory and decision theory as mentioned in this paper.Abstract:
Many singularities, bifurcations, and catastrophes (jumps) arise in all maxima and minima problems ; such problem arise, for instance, 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). On smooth change of the function the optimum solution changes with a jump, transferring from one competing maxima (A) to the other (B).read more
Citations
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Singularities and Catastrophes in Economics: Historical Perspectives and Future Directions
TL;DR: In this paper, the authors look at the historical context of singularities through the work of two eminent Frenchmen around the late 1960s and 1970s, Ren\'e Thom (1923-2002) and G\'erard Debreu (1921-2004), who would receive the Nobel Prize in economics in 1983.
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Singularities and Catastrophes in Economics: Historical Perspectives and Future Directions
TL;DR: In this paper, the authors look at the historical context of singularities through the work of two eminent Frenchmen around the late 1960s and 1970s, Rene Thom (1923-2002) and Gerard Debreu (1921-2004), who would receive the Nobel Prize in economics in 1983.
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Journal ArticleDOI
Asymptotic exponential integrals, Newton's diagram, and the classification of minimal points
TL;DR: In this article, the problem of finding the asymptotics as h ÷ + 0 of the volume of the set is reduced to the question of computing the volume in the set.