Davydov, Aleksej A.; Zakalyukin, Vladimir M. 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]. Reviewer: Chandra Shekhar Sharma (London) Cited in 2 Documents 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 Keywords:Control theory; parametric optimisation; extremal problems; attainability PDFBibTeX XMLCite \textit{A. A. Davydov} and \textit{V. M. Zakalyukin}, Banach Cent. Publ. 50, 75--90 (1999; Zbl 1040.65052) Full Text: EuDML