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

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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.

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Authors and Affiliations

  1. Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia

    Yu. G. Evtushenko

  2. Institute for System Analysis, Russian Academy of Sciences, pr. 60-letiya Oktyabrya 9, Moscow, 117312, Russia

    M. A. Posypkin

Authors
  1. Yu. G. Evtushenko
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  2. M. A. Posypkin
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Correspondence to Yu. G. Evtushenko.

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Original Russian Text © Yu.G. Evtushenko, M.A. Posypkin, 2011, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2011, Vol. 51, No. 8, pp. 1376–1389.

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Evtushenko, Y.G., Posypkin, M.A. An application of the nonuniform covering method to global optimization of mixed integer nonlinear problems. Comput. Math. and Math. Phys. 51, 1286–1298 (2011). https://doi.org/10.1134/S0965542511080082

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