Geodesic
Reduced-direction methods with feasible points in nonlinear programming
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 2, pp. 217-230 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

An approach to the construction of feasible direction type methods of nonlinear programming is proposed. The approach relies on linearization of the active constraints, which reduces the problem of choosing a direction of descent of the objective function inside the feasible region to an unconstrained direction-choosing problem for an auxiliary function in a lower-dimensional space. The approach is developed for problems with inequality constraints and extended to problems with both inequality and equality constraints. 
@article{ZVMMF_1990_30_2_a4,
     author = {V. S. Izhutkin and M. Yu. Kokurin},
     title = {Reduced-direction methods with feasible points in nonlinear programming},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {217--230},
     year = {1990},
     volume = {30},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_2_a4/}
}
TY  - JOUR
AU  - V. S. Izhutkin
AU  - M. Yu. Kokurin
TI  - Reduced-direction methods with feasible points in nonlinear programming
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 1990
SP  - 217
EP  - 230
VL  - 30
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_2_a4/
LA  - ru
ID  - ZVMMF_1990_30_2_a4
ER  - 
%0 Journal Article
%A V. S. Izhutkin
%A M. Yu. Kokurin
%T Reduced-direction methods with feasible points in nonlinear programming
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 1990
%P 217-230
%V 30
%N 2
%U http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_2_a4/
%G ru
%F ZVMMF_1990_30_2_a4
V. S. Izhutkin; M. Yu. Kokurin. Reduced-direction methods with feasible points in nonlinear programming. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 2, pp. 217-230. http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_2_a4/

[1] Izhutkin V. S., Kokurin M. Yu., “Metody privedennykh napravlenii dlya reshenii zadach nelineinogo programmirovaniya”, Zh. vychisl. matem. i matem. fiz., 28:12 (1988), 1799–1814 | MR

[2] Schönefeld K., “Ein hybrides Verfahren der nichtlinearen Optimierung”, Seminarberichte Humboldt-Univ. Berlin. Sekt. Math., 50 (1983), 308–316

[3] Pshenichnyi B. N., Metod linearizatsii, Nauka, M., 1983 | MR

[4] Izhutkin V. S., “Ob ispolzovanii ellipsoidnoi normalizatsii pri reshenii zadach vybora napravleniya v metode linearizatsii”, Vestn. MGU. Ser. 15, 1988, no. 3, 43–49 | MR

[5] Gill F., Myurrei U., Rait M., Prakticheskaya optimizatsiya, Mir, M., 1985 | MR

[6] Pshenichnyi B. N., Danilin Yu. M., Chislennye metody v ekstremalnykh zadachakh, Nauka, M., 1975 | MR | Zbl

[7] Karmanov V. G., Matematicheskoe programmirovanie, Nauka, M., 1986 | MR

[8] Maistrovskii G. D., Olkhovskii Yu. G., “O skorosti skhodimosti metoda naiskoreishego spuska v zadache uslovnoi minimizatsii”, Zh. vychisl. matem. i matem. fiz., 15:4 (1975), 844–859 | MR | Zbl

[9] Bulatov V. P., Metody pogruzheniya v zadachakh optimizatsii, Nauka, Novosibirsk, 1977 | MR | Zbl

[10] Mayne D. Q., Polak E., “Feasible directions algorithms for optimization problems with equality and inequality constraints”, Math. Program., 11:1 (1976), 67–80 | DOI | MR | Zbl

[11] Schönefeld K., “A note on a globalization of Wilson-type optimization methods”, Computing, 37:2 (1986), 171–178 | DOI | MR

[12] Kokurin M. Yu., “Ob odnoi modifikatsii proektsionnogo metoda dlya obschei zadachi nelineinogo programmirovaniya”, Metody matem. programmirovaniya i programmnoe obespechenie, Tezisy dokl. V konf., Sverdlovsk, 1987, 67–68

[13] Bertsekas D., Uslovnaya optimizatsiya i metody mnozhitelei Lagranzha, Radio i svyaz, M., 1987 | MR | Zbl

[14] Ishutkin V. S., Schönefeld K., “On the globalization of Wilson-type optimization methods by means of generalized reduced gradient methods”, Computing, 37:2 (1986), 151–169 | DOI | MR | Zbl