Necessary conditions for an extremum in 2-regular problems

The necessary conditions for local extremum in 2-regular problems are studied. The necessary conditions for an extremum that uses the Lagrangian function L are generally invalid. The generalization gives no additional information on the irregular situation, since the corresponding first-order necessary condition in automatically satisfied with λ= 0, irrespective of f. The first and second-order necessary conditions for a local extremum were obtained by using the Lagrange functions, in the irregular case for a problem with equality constrain. The necessary conditions for a local extremum are first-order conditions, as they use only the first derivatives of the objective function f. The function f is twice Frechet differentiable at x and the function F is thrice Frechet differentiable at the second order necessary conditions.

Authors
Avakov E.R.1 , Arutyunov A.V. 2 , Izmailov A.F.3
Number of issue
3
Language
English
Pages
340-343
Status
Published
Volume
73
Year
2006
Organizations
  • 1 Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Profsoyuznaya ul. 65, Moscow, 117997, Russian Federation
  • 2 Russian University of Peoples' Friendship, ul. Miklukho-Maklaya 6, Moscow, 117198, Russian Federation
  • 3 Faculty of Computational Mathematics and Cybernetics, Moscow State University, Leninskie gory, Moscow, 119992, Russian Federation
Keywords
Differentiation (calculus); Function evaluation; Lagrange multipliers; Number theory; Frechet differentiable; Generalization; Lagrangian function; Problem solving
Date of creation
19.10.2018
Date of change
19.10.2018
Short link
https://repository.rudn.ru/en/records/article/record/3374/
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