Continuous Variable Neighborhood Search (C-VNS) for Solving Systems of Nonlinear Equations

Jun Pei (), Zorica Dražić (), Milan Dražić (), Nenad Mladenović () and Panos M. Pardalos ()
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Jun Pei: School of Management, Hefei University of Technology, Hefei 230009, China
Zorica Dražić: Faculty of Mathematics, University of Belgrade, Belgrade 11000, Serbia
Milan Dražić: Faculty of Mathematics, University of Belgrade, Belgrade 11000, Serbia
Nenad Mladenović: Emirates College of Technology, Abu Dhabi 41009, United Arab Emirates, Ural Federal University, Yekaterinburg 620083, Russia
Panos M. Pardalos: Center for Applied Optimization, Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida 32611-6595

INFORMS Journal on Computing, 2019, vol. 31, issue 2, 235-250

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: system of nonlinear equations; continuous optimization; variable neighborhood search; direct search methods (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:inm:orijoc:v:31:y:2019:i:2:p:235-250

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