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Classification of relative minima singularities. (English) Zbl 1040.65052

Janeczko, Stanisław (ed.) et al., Geometry and topology of caustics – CAUSTICS ’98. Proceedings of the Banach Center symposium, Warsaw, Poland, June 15–27, 1998. Warsaw: Polish Academy of Sciences, Institute of Mathematics. Banach Cent. Publ. 50, 75-90 (1999).
Continuing their earlier work on the singularities of extrema, the authors present a classification of relative minima singularities for a wide variety of settings in parametric optimisation theory. Reversing the sign of a minimising function one gets the corresponding results for relative maxima. The work aims to clarify the close interconnections between the singularities of a function on a manifold with boundary, discriminants for simple projections, singularities of diagrams of mappings and flag-contact simple germs.
For the entire collection see [Zbl 0931.00034].

MSC:

65K10 Numerical optimization and variational techniques
83C25 Approximation procedures, weak fields in general relativity and gravitational theory
58K25 Stability theory for manifolds
58K30 Global theory of singularities
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