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Minimizing a Symmetric Quasiconvex Function on a Two-Dimensional Lattice

Journal of Applied and Industrial Mathematics. 2018. Vol. 12. No. 3. P. 587-594.
Веселов С. И., Gribanov D., Zolotykh N., Чирков А. Ю.

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.