Continuous Variable Neighborhood Search (C-VNS) for Solving Systems of Nonlinear Equations
Jun Pei, Zorica Dražić, Milan Dražić, Nenad Mladenović, Panos M. Pardalos
INFORMS Journal on Computing · 2019 · Volume 31 · Issue 2
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. The online supplement is available at https://doi.org/10.1287/ijoc.2018.0876 .
Keywords
system of nonlinear equations, continuous optimization, variable neighborhood search, direct search methods
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