Geodesic
On the Second Order Sufficient Optimality Conditions for a Problem of Mathematical Programming
Matematičeskie zametki, Tome 115 (2024) no. 2, pp. 177-196.

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider the constrained optimization problem for a smooth function defined on a Banach space with smooth constraints of equality and inequality type. We show that for this problem, under the known sufficient second-order optimality conditions, the set of Lagrange multipliers can be replaced by a smaller set.
Keywords: mathematical programming problem, Lagrange function, sufficient second-order optimality conditions. 
@article{MZM_2024_115_2_a2,
     author = {A. V. Arutyunov and S. E. Zhukovskiy},
     title = {On the {Second} {Order} {Sufficient} {Optimality} {Conditions} for a {Problem} of {Mathematical} {Programming}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {177--196},
     publisher = {mathdoc},
     volume = {115},
     number = {2},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2024_115_2_a2/}
}
TY  - JOUR
AU  - A. V. Arutyunov
AU  - S. E. Zhukovskiy
TI  - On the Second Order Sufficient Optimality Conditions for a Problem of Mathematical Programming
JO  - Matematičeskie zametki
PY  - 2024
SP  - 177
EP  - 196
VL  - 115
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2024_115_2_a2/
LA  - ru
ID  - MZM_2024_115_2_a2
ER  - 
%0 Journal Article
%A A. V. Arutyunov
%A S. E. Zhukovskiy
%T On the Second Order Sufficient Optimality Conditions for a Problem of Mathematical Programming
%J Matematičeskie zametki
%D 2024
%P 177-196
%V 115
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2024_115_2_a2/
%G ru
%F MZM_2024_115_2_a2
A. V. Arutyunov; S. E. Zhukovskiy. On the Second Order Sufficient Optimality Conditions for a Problem of Mathematical Programming. Matematičeskie zametki, Tome 115 (2024) no. 2, pp. 177-196. http://geodesic.mathdoc.fr/item/MZM_2024_115_2_a2/

[1] V. M. Alekseev, V. M. Tikhomirov, S. V. Fomin, Optimalnoe upravlenie, Fizmatlit, M. 2007, 2007 | MR

[2] F. P. Vasilev, Metody optimizatsii, v. 1, MTsNMO, M., 2011

[3] A. V. Arutyunov, “Gladkie anormalnye zadachi teorii ekstremuma i analiza”, UMN, 67:3 (405) (2012), 3–62 | DOI | MR | Zbl

[4] D. Klatte, B. Kummer, Nonsmooth Equations in Optimization. Regularity, Calculus, Methods and Applications, Nonconvex Optim. Appl., 60, Kluwer Acad. Publ., Dordrecht, 2002 | MR

[5] J. F. Bonnans, A. Shapiro, Perturbation Analysis of Optimization Problems, Springer Ser. Oper. Res., Springer, New York, 2000 | MR

[6] D. Yu. Karamzin, “Neobkhodimye usloviya ekstremuma v zadache upravleniya s fazovymi ogranicheniyami”, Zh. vychisl. matem. i matem. fiz., 47:7 (2007), 1123–1150 | MR

[7] B. S. Mordukhovich, M. E. Sarabi, “Critical multipliers in variational systems via second-order generalized differentiation”, Math. Program., 169:2 (2018), 605–648 | DOI | MR

[8] B. S. Mordukhovich, M. E. Sarabi, “Second-order analysis of piecewise linear functions with applications to optimization and stability”, J. Optim. Theory Appl., 171:2 (2016), 504–526 | DOI | MR

[9] A. F. Izmailov, Chuvstvitelnost v optimizatsii, FIZMATLIT, M., 2006

[10] A. F. Izmailov, “Chuvstvitelnost reshenii sistem uslovii optimalnosti pri narushenii uslovii regulyarnosti ogranichenii”, Zh. vychisl. matem. i matem. fiz., 47:4 (2007), 555–577 | MR | Zbl

[11] A. V. Arutyunov, “Polozhitelnost kvadratichnykh form na peresechenii kvadrik”, Matem. zametki, 71:1 (2002), 27–36 | DOI | MR | Zbl

[12] R. Khille, E. Fillips, Funktsionalnyi analiz i polugruppy, IL, M., 1962 | MR