Geodesic
Exact auxiliary functions in optimization problems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 1, pp. 43-57 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The concept of an exact auxiliary function such that the problem of minimizing it has the same set of solutions as the original optimization problem. Sufficient conditions are given for the auxiliary functions to be exact and examples of such functions are described. The introduction of exact auxiliary functions makes it possible to reduce the solution of the original problem to single minimization of an auxiliary function. The constrained optimization problem often reduces to unconstrained optimization. 
@article{ZVMMF_1990_30_1_a4,
     author = {Yu. G. Evtushenko and V. G. Zhadan},
     title = {Exact auxiliary functions in optimization problems},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {43--57},
     year = {1990},
     volume = {30},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_1_a4/}
}
TY  - JOUR
AU  - Yu. G. Evtushenko
AU  - V. G. Zhadan
TI  - Exact auxiliary functions in optimization problems
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 1990
SP  - 43
EP  - 57
VL  - 30
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_1_a4/
LA  - ru
ID  - ZVMMF_1990_30_1_a4
ER  - 
%0 Journal Article
%A Yu. G. Evtushenko
%A V. G. Zhadan
%T Exact auxiliary functions in optimization problems
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 1990
%P 43-57
%V 30
%N 1
%U http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_1_a4/
%G ru
%F ZVMMF_1990_30_1_a4
Yu. G. Evtushenko; V. G. Zhadan. Exact auxiliary functions in optimization problems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 1, pp. 43-57. http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_1_a4/

[1] Eremin I. I., “Metod “shtrafov” v vypuklom programmirovanii”, Dokl. AN SSSR, 173:4 (1967), 748–751 | MR | Zbl

[2] Zangwill W., “Non-linear programming via penalty function”, Manag. Sci, 1967, 344–358 | DOI | MR | Zbl

[3] Skarin V. D., “Ob odnoi modifikatsii metoda shtrafnykh funktsii v vypuklom programmirovanii”, Nelineinaya optimizatsiya i prilozheniya v planirovanii, UNTs AN SSSR, Sverdlovsk, 1973, 51–62 | MR

[4] Evans J. P., Gould F. J., Tolle J. W., “Exact penalty functions in nonlinear programming”, Math. Program., 4 (1973), 72–97 | DOI | MR | Zbl

[5] Golikov A. I., “Metod vneshnikh tsentrov i negladkie shtrafnye funktsii”, Sistemy programmnogo obespecheniya resheniya zadach optimalnogo planirovaniya, VII Vses. simpozium, M., 1982, 125–126

[6] Evtushenko Yu. G., “Otsenki tochnosti v metodakh shtrafnykh funktsii”, Probl. prikl. matem. i informatiki, Nauka, M., 1987, 199–208 | MR

[7] Zhadan V. G., “O nekotorykh otsenkakh koeffitsienta shtrafa v metodakh tochnykh shtrafnykh funktsii”, Zh. vychisl. matem. i matem. fiz., 24:8 (1984), 1164–1171 | MR | Zbl

[8] Evtushenko Yu. G., Zhadan V. G., “K voprosu o sistematizatsii chislennykh metodov nelineinogo programmirovaniya. Metody posledovatelnoi bezuslovnoi minimizatsii”, Soobsch. po prikl. matem., VTs AN SSSR, M., 1988 | MR

[9] Evtushenko Yu. G., Metody resheniya ekstremalnykh zadach i ikh primenenie v sistemakh optimizatsii, Nauka, M., 1982 | MR | Zbl

[10] Han S.-P., Mangasarian O. L., “Exact penalty functions in nonlinear programming”, Math. Program., 17 (1979), 251–269 | DOI | MR

[11] Morrison D. D., “Optimization by least squares”, SIAM J. Numer. Analys., 5:1 (1968), 83–88 | DOI | MR | Zbl