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Approximating a solution set of nonlinear inequalities

Author

Listed:
  • Yuri Evtushenko

    (National Research University Higher School of Economics
    Federal Research Center Computer Science and Control of Russian Academy of Sciences)

  • Mikhail Posypkin

    (National Research University Higher School of Economics
    Federal Research Center Computer Science and Control of Russian Academy of Sciences)

  • Larisa Rybak

    (Belgorod State Technological University named after V.G. Shukhov)

  • Andrei Turkin

    (Federal Research Center Computer Science and Control of Russian Academy of Sciences
    National Research University of Electronic Technology)

Abstract

In this paper we propose a method for solving systems of nonlinear inequalities with predefined accuracy based on nonuniform covering concept formerly adopted for global optimization. The method generates inner and outer approximations of the solution set. We describe the general concept and three ways of numerical implementation of the method. The first one is applicable only in a few cases when a minimum and a maximum of the constraints convolution function can be found analytically. The second implementation uses a global optimization method to find extrema of the constraints convolution function numerically. The third one is based on extrema approximation with Lipschitz under- and overestimations. We obtain theoretical bounds on the complexity and the accuracy of the generated approximations as well as compare proposed approaches theoretically and experimentally.

Suggested Citation

  • Yuri Evtushenko & Mikhail Posypkin & Larisa Rybak & Andrei Turkin, 2018. "Approximating a solution set of nonlinear inequalities," Journal of Global Optimization, Springer, vol. 71(1), pages 129-145, May.
    • Handle: RePEc:spr:jglopt:v:71:y:2018:i:1:d:10.1007_s10898-017-0576-z
    DOI: 10.1007/s10898-017-0576-z
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    Cited by:

    1. Lera, Daniela & Posypkin, Mikhail & Sergeyev, Yaroslav D., 2021. "Space-filling curves for numerical approximation and visualization of solutions to systems of nonlinear inequalities with applications in robotics," Applied Mathematics and Computation, Elsevier, vol. 390(C).

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