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JOURNALS // Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki // Archive

Zh. Vychisl. Mat. Mat. Fiz., 2025 Volume 65, Number 3, Pages 301–324 (Mi zvmmf11938)

Optimal control

Application of interval slopes in nonsmooth one-dimensional optimization problems

M. A. Posypkinab, D. A. Sidnevc

a Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 119333, Moscow, Russia
b Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, 119991, Moscow, Russia
c National Research University of Electronic Technology (MIET), 124498, Zelenograd, Moscow, Russia

Abstract: The interval interpretation of a first-order divided difference, namely, interval slope is considered. Some properties of interval slopes, including ones for convex (concave) functions are proved. Based on the interval slope, necessary and sufficient conditions for the monotonicity of a function are formulated and proved. These criteria are used to propose an algorithm for the global optimization of a one-variable function taking into account its monotonicity. Numerical experiments are conducted that show that the developed global optimization method is applicable in the nondifferentiable case and significantly accelerates finding an approximate global optimum as compared with the basic version.

Key words: global optimization, deterministic optimization methods, interval analysis, interval slope, monotonicity criteria.

UDC: 519.65

Received: 30.08.2024
Revised: 02.12.2024
Accepted: 12.12.2024

DOI: 10.31857/S0044466925030068


 English version:
Computational Mathematics and Mathematical Physics, 2025, 65:3, 544–566

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© Steklov Math. Inst. of RAS, 2025