E. R. Avakov, A. V. Arutyunov, D. Yu. Karamzin, “An investigation of smooth maps in a neighbourhood of an abnormal point”, Izv. RAN. Ser. Mat., 2014, Volume 78, Issue 2,Pages <nobr>3

This article is cited in 7 papers

An investigation of smooth maps in a neighbourhood of an abnormal point

E. R. Avakov^a, A. V. Arutyunov^bc, D. Yu. Karamzin^d

^a Institute of Control Sciences, Russian Academy of Sciences, Moscow
^b Peoples Friendship University of Russia
^c M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
^d Dorodnitsyn Computing Centre of the Russian Academy of Sciences, Moscow

Abstract: We study the solubility of systems of non-linear equations in a neighbourhood of an abnormal point and prove inverse function theorems that guarantee the existence of solutions satisfying a linear-root estimate in the neighbourhood of the abnormal point. We also address the related issue of necessary conditions for an extremum at an abnormal point in a finite-dimensional constrained problem. We obtain second-order necessary optimality conditions that improve the known results.

Keywords: inverse function theorem, abnormal point, conditional extremum problem.

UDC: 517.9

MSC: 26B10, 49K27

Received: 14.10.2011
Revised: 04.06.2013

DOI: 10.4213/im7928