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Second-order conditions in extremal problems. The abnormal points


Author: A. V. Arutyunov
Journal: Trans. Amer. Math. Soc. 350 (1998), 4341-4365
MSC (1991): Primary 49B27
DOI: https://doi.org/10.1090/S0002-9947-98-01775-9
MathSciNet review: 1390966
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Abstract: In this paper we study a minimization problem with constraints and obtain first- and second-order necessary conditions for a minimum. Those conditions - as opposed to the known ones - are also informative in the abnormal case. We have introduced the class of 2-normal constraints and shown that for them the ``gap" between the sufficient and the necessary conditions is as minimal as possible. It is proved that a 2-normal mapping is generic.


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Additional Information

A. V. Arutyunov
Affiliation: Department of Differentional Equations and Functional Analysis, Peoples Friendship University of Russia, Moscow 117198, Mikluka-Maklai, 6, Russia
Email: arutunov@sa640.cs.msu.su

DOI: https://doi.org/10.1090/S0002-9947-98-01775-9
Keywords: Abnormal point, Lagrange multipliers, second-order necessary conditions, index of quadratic form, 2-normal mapping
Received by editor(s): January 25, 1995
Received by editor(s) in revised form: September 20, 1995
Additional Notes: This work was supported by Russian Fund of Fundamental Researches, project N 96-01-00800 and partially by Grant of Goskomvuz of Russia, project N 95-0-1.9-48
Article copyright: © Copyright 1998 American Mathematical Society