Investigation of dimensionality reduction schemes for an algorithm for finding the zero value of a non-negative function

Title	Investigation of dimensionality reduction schemes for an algorithm for finding the zero value of a non-negative function
Authors	A. S. Zaitsev¹, K. A. Barkalov¹ ¹Lobachevsky State University of Nizhny Novgorod
Annotation	The paper addresses the problem of finding the global minimum of a multidimensional multiextremal function that takes non-negative values and attains zero within its domain. Such a problem can be interpreted as minimizing the residual between theoretical and experimental data. To accelerate the convergence of an algorithm for locating the zero of a non-negative multidimensional function, it is proposed to reduce the dimensionality of the problem using an approximation of the Peano curve – a non-injective evolvent. Computational experiments have been carried out confirming the effectiveness of the proposed approach to dimensionality reduction in this problem.
Keywords	global optimization, dimensionality reduction, Peano curves, zero value of a function.
Citation	Zaitsev A. S., Barkalov K. A. ''Investigation of dimensionality reduction schemes for an algorithm for finding the zero value of a non-negative function'' [Electronic resource]. Mathematical modeling, numerical methods, and software systems: Collection of materials from the 12th All‑Russian Scientific Youth School‑Seminar named after E. V. Voskresensky (Saransk, July 21–24, 2026). - pp. 83-88. Available at: https://conf.svmo.ru/files/2026/papers/paper79.pdf. - Date of access: 25.09.2026.