Authors: Pei, Jun
Dražić, Zorica
Dražić, Milan
Mladenović, Nenad 
Pardalos, Panos
Title: Continuous variable neighborhood search (C-VNS) for solving systems of nonlinear equations
Journal: INFORMS Journal on Computing
Volume: 31
Issue: 2
First page: 235
Last page: 250
Issue Date: 1-Jan-2019
Rank: M22
ISSN: 1091-9856
DOI: 10.1287/ijoc.2018.0876
Abstract: 
In this paper, we propose the continuous variable neighborhood search method for finding all the solutions to a nonlinear system of equations (NSEs). We transform the NSE problem into an equivalent optimization problem, and we use a new objective function that allows us to find all the zeros. Instead of the usual sum-of-squares objective function, our objective function is presented as the sum of absolute values. Theoretical investigation confirms that our objective function provides more accurate solutions regardless of the optimization method used. In addition, we achieve a trade-off (i.e., increased precision at the expense of reduced smoothness). Computational analysis of standard test instances shows that the proposed method is more precise and much faster than two recently developed methods. Similar conclusions are drawn by comparing the proposed method with many other methods in the literature.
Keywords: Continuous optimization | Direct search methods | System of nonlinear equations | Variable neighborhood search
Publisher: INFORMS
Project: National Natural Science Foundation of China (Grants 71871080, 71601065, 71690235,71501058, and 71521001)
Humanities and Social Sciences Foundation of the Chinese Ministry of Education (Grant 15YJC630097)
“Development of information technologies and systems for stimulation of personality’s sustainable development as one of the bases of development of digital Kazakhstan”, Grant BR05236839

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