Geodesic
An application of the nonuniform covering method to global optimization of mixed integer nonlinear problems
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 8, pp. 1376-1389 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The nonuniform covering method for global optimization of functions of several variables is extended to nonlinear programs. It is shown that this method can be used for solving problems that, in addition to conventional constraints, involve partial integrality conditions. Estimates for the accuracy of the solution and for the number of steps required for finding a minimum with a prescribed tolerance are derived. New minorants based on an estimate for the spectrum of the Hessian matrix of the objective function and the constraints are given. New formulas for covering sets improving the efficiency of the method are obtained. Examples of solving nonlinear programs with the use of the proposed approach are presented. 
@article{ZVMMF_2011_51_8_a2,
     author = {Yu. G. Evtushenko and M. A. Posypkin},
     title = {An application of the nonuniform covering method to global optimization of mixed integer nonlinear problems},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1376--1389},
     year = {2011},
     volume = {51},
     number = {8},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_8_a2/}
}
TY  - JOUR
AU  - Yu. G. Evtushenko
AU  - M. A. Posypkin
TI  - An application of the nonuniform covering method to global optimization of mixed integer nonlinear problems
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2011
SP  - 1376
EP  - 1389
VL  - 51
IS  - 8
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_8_a2/
LA  - ru
ID  - ZVMMF_2011_51_8_a2
ER  - 
%0 Journal Article
%A Yu. G. Evtushenko
%A M. A. Posypkin
%T An application of the nonuniform covering method to global optimization of mixed integer nonlinear problems
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2011
%P 1376-1389
%V 51
%N 8
%U http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_8_a2/
%G ru
%F ZVMMF_2011_51_8_a2
Yu. G. Evtushenko; M. A. Posypkin. An application of the nonuniform covering method to global optimization of mixed integer nonlinear problems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 8, pp. 1376-1389. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_8_a2/

[1] Evtushenko Yu. G., “Chislennyi metod poiska globalnogo ekstremuma funktsii (perebor na neravnomernoi setke)”, Zh. vychisl. matem. i matem. fiz., 11:6 (1971), 1390–1403 | Zbl

[2] Evtushenko Yu. G., Ratkin V. A., “Metod polovinnykh delenii dlya globalnoi optimizatsii funktsii mnogikh peremennykh”, Tekhn. kibernetika, 1987, no. 1, 119–127 | MR | Zbl

[3] Evtushenko Yu. G., Potapov M. A., Korotkikh V. V., “Numerical methods for global optimization”, Recent advances in global optimization (Princeton, NJ, 1991), Princeton Ser. Comput. Sci., Princeton Univ. Press, Princeton, NJ, 1992, 274–297 | MR

[4] Ratchek H., Rokne J., New computer methods for global optimization, Ellis Horwood, Chichester, 1988

[5] Evtushenko Yu. G., Malkova V. U., Stanevichyus A. A., “Parallelnyi poisk globalnogo ekstremuma funktsii mnogikh peremennykh”, Zh. vychisl. matem. i matem. fiz., 49:2 (2009), 255–269 | MR | Zbl

[6] Evtushenko Y., Posypkin M., Sigal I., “A framework for parallel large-scale global optimization”, Comput. Sci. – Res. and Development, 23:3 (2009), 211–215 | DOI

[7] Evtushenko Yu. G., Potapov M. A., “Metody resheniya mnogokriterialnykh zadach”, Dokl. AN SSSR, 291:1 (1986), 25–39 | MR

[8] Posypkin M. A., “Reshenie zadach globalnoi optimizatsii v srede raspredelennykh vychislenii”, Programmnye produkty i sistemy, 2010, no. 1, 23–29 | MR

[9] Tawarmalani M., Sahinidis N. V., “A polyhedral branch-and-cut approach to global optimization”, Math. Program., 103:2 (2005), 225–249 | DOI | MR | Zbl

[10] http://www.lindo.com/

[11] http://www.gams.com/

[12] Evans J. P., Gould F. J., “Stability in nonlinear programming”, Operat. Res., 18 (1970), 107–118 | DOI | MR | Zbl

[13] Golikov A. I., Kotkin G. G., “Kharakteristika mnozhestva optimalnykh otsenok zadachi mnogokriterialnoi optimizatsii”, Zh. vychisl. matem. i matem. fiz., 28:10 (1988), 1461–1474 | MR | Zbl

[14] Tyrtyshnikov E. E., Matrichnyi analiz i lineinaya algebra, Fizmatlit, M., 2007

[15] Tuy H., “D(C)-optimization and robust global optimization”, J. Global Optimizat., 47 (2010), 485–501 | DOI | MR | Zbl