Second–order Conditions in Extremal Problems. the Abnormal Points

  title={Second–order Conditions in Extremal Problems. the Abnormal Points},
  author={Aram V. Arutyunov},
In this paper we study a minimization problem with constraints and obtain firstand 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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Publications referenced by this paper.
Showing 1-10 of 15 references

Arutyunov, “The Level Set of a Smooth Mapping in a Neighbourhood of a Singular Point and the Zeros of a Quadratic Mapping

E. R. Avakov, A.V.A.A. Agrachev
Mat. Sb., • 1991

Necessary Extremal Conditions for Abnormal Problem with Constraints of Equality Type

A. V. Arutyunov
Usp. Mat. Nauk, • 1990

Another Condition for a Conditional Extremum

A. A. Agrachev
Usp. Mat. Nauk, • 1989

Necessary Extremum Conditions for Smooth Abnormal Problem with Equality and Inequality-type Constraints

A. R. Avakov
Mat. Zametki, • 1989

Perturbations of Extremal Problems with Constraints and Necessary Conditions of Optimality

A. V. Arutyunov
Itogi Nauki i Tekhniki. Ser. Matem. Analiz, • 1989

V.M.Tikhomirov and S.V.Fomin, Optimal Control, Consultants

V. M. Alekseev
MR 89e:49002 • 1987

Conditions for an Extremum for Smooth Problems with Constraints of Equality Type

E. R. Avakov
English transl., USSR Comput. Math. and Math. Phys • 1985

Gusein-Zade, Singularities of Differentiable Mappings, [in Russian] Nauka, Moscow (1982)

V. I. Arnold, S.M.A.N. Varchenko
English transl., Birkhäuser, • 1985

On Necessary Conditions of Optimality Problem with Phase Constraints

A. V. Arutyunov
Dokl. Akad. Nauk SSSR, • 1985

Tynyanskii, “On Necessary Conditions for a Local Minimum in Optimal Control Theory

N.T.A.V. Arutyunov
Dokl. Akad. Nauk SSSR, 275, • 1984

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