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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2011, Volume 51, Number 8, Pages 1376–1389 (Mi zvmmf9520)  
This article is cited in 18 scientific papers (total in 18 papers)

An application of the nonuniform covering method to global optimization of mixed integer nonlinear problems

Yu. G. Evtushenkoa, M. A. Posypkinb

a Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333 Russia
b Institute for System Analysis, Russian Academy of Sciences, pr. 60-letiya Oktyabrya 9, Moscow, 117312 Russia
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Abstract: 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.
Key words: global optimization, nonlinear programming, mixed integer problems, sensitivity function, nonuniform covering method, numerical methods of optimization.
Received: 15.02.2011
English version:
Computational Mathematics and Mathematical Physics, 2011, Volume 51, Issue 8, Pages 1286–1298
DOI: https://doi.org/10.1134/S0965542511080082
Bibliographic databases:
Document Type: Article
UDC: 519.658.4
Language: Russian
Citation: Yu. G. Evtushenko, M. A. Posypkin, “An application of the nonuniform covering method to global optimization of mixed integer nonlinear problems”, Zh. Vychisl. Mat. Mat. Fiz., 51:8 (2011), 1376–1389; Comput. Math. Math. Phys., 51:8 (2011), 1286–1298
Citation in format AMSBIB
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    • This publication is cited in the following 18 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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