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

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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. 
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     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},
     publisher = {mathdoc},
     volume = {51},
     number = {8},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_8_a2/}
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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/