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

Posted: 30 Jul 2018

See all articles by Jun Pei

Jun Pei

The School of Management, Hefei University of Technology; University of Florida - Department of Industrial and Systems Engineering

Zorica Darzic

Faculty of Mathematics, University of Belgrade

Milan Drazic

Faculty of Mathematics, University of Belgrade

Nenad Mladenovic

Mathematical Institute, Serbian Academy of Sciences and Arts

Panos Pardalos

University of Florida

Date Written: July 8, 2018

Abstract

In this paper we propose C-VNS (Continuous variable neighborhood search) method for finding all solutions to a nonlinear system of equations (NSE). We transform the NSE problem into an equivalent optimization problem, and we use a new objective function that allows us to find all 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, irrespective of what optimization method is used. We sacrifice the smoothness property to increase precision. Computational analysis on standard test instances shows that our C-VNS based method is more precise and much faster than the two recent methods from the literature, we compared with. Moreover, similar conclusions are derived after comparing our C-VNS based heuristic with many other methods from the literature.

Keywords: System of Nonlinear Equations, Continuous Optimization, Variable Neighborhood Search, Direct Search Method

Suggested Citation

Pei, Jun and Darzic, Zorica and Drazic, Milan and Mladenovic, Nenad and Pardalos, Panos, Continuous Variable Neighborhood Search (C-VNS) for Solving Systems of Nonlinear Equations (July 8, 2018). Available at SSRN: https://ssrn.com/abstract=3210369

Jun Pei (Contact Author)

The School of Management, Hefei University of Technology ( email )

193 Tunxi Road
Hefei, Anhui 230009
China

University of Florida - Department of Industrial and Systems Engineering ( email )

401 Weil Hall
Gainesville, FL Florida 116595
United States

Zorica Darzic

Faculty of Mathematics, University of Belgrade ( email )

Knez Mihajlova 36/III Srbija
Belgrade, Belgrade 111111
Serbia

Milan Drazic

Faculty of Mathematics, University of Belgrade ( email )

Knez Mihajlova 36/III Srbija
Belgrade, Belgrade 111111
Serbia

Nenad Mladenovic

Mathematical Institute, Serbian Academy of Sciences and Arts ( email )

Knez Mihajlova 36/III Srbija
Belgrade, Belgrade 11000
Serbia

Panos Pardalos

University of Florida ( email )

PO Box 117165, 201 Stuzin Hall
Gainesville, FL 32610-0496
United States

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