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Second-order conditions in extremal problems. The abnormal points
Author(s):
A.
V.
Arutyunov
Journal:
Trans. Amer. Math. Soc.
350
(1998),
4341-4365.
MSC (1991):
Primary 49B27
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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:
10.1090/S0002-9947-98-01775-9
PII:
S 0002-9947(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
Copyright of article:
Copyright
1998,
American Mathematical Society
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