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Minimizing a Symmetric Quasiconvex Function on a Two-Dimensional Lattice

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Abstract

We consider the minimization problem for a symmetric quasiconvex function defined by an oracle on the set of integer points of a square. We formulate an optimality criterion for the solution, obtain a logarithmic lower bound for the complexity of the problem, and propose an algorithm for which the number of inquiries to the oracle is at most thrice the lower bound.

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Authors and Affiliations

  1. Institute of Information Technology, Mathematics, and Mechanics, Lobachevsky Nizhny Novgorod State University, pr. Gagarina 23, Nizhny Novgorod, 603950, Russia

    S. I. Veselov, D. B. Gribanov, N. Yu. Zolotykh & A. Yu. Chirkov

Authors
  1. S. I. Veselov
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  2. D. B. Gribanov
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  3. N. Yu. Zolotykh
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  4. A. Yu. Chirkov
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Corresponding author

Correspondence to S. I. Veselov.

Additional information

Original Russian Text © S.I. Veselov, D.V. Gribanov, N.Yu. Zolotykh, A.Yu. Chirkov, 2018, published in Diskretnyi Analiz i Issledovanie Operatsii, 2018, Vol. 25, No. 3, pp. 23–35.

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Veselov, S.I., Gribanov, D.B., Zolotykh, N.Y. et al. Minimizing a Symmetric Quasiconvex Function on a Two-Dimensional Lattice. J. Appl. Ind. Math. 12, 587–594 (2018). https://doi.org/10.1134/S199047891803016X

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  • DOI: https://doi.org/10.1134/S199047891803016X

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