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A new approach for solving nonlinear equations systems
 IEEE Transactions on Systems, Man and Cybernetics Part A
"... Abstract—This paper proposes a new perspective for solving systems of complex nonlinear equations by simply viewing them as a multiobjective optimization problem. Every equation in the system represents an objective function whose goal is to minimize the difference between the right and left terms o ..."
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Cited by 15 (3 self)
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Abstract—This paper proposes a new perspective for solving systems of complex nonlinear equations by simply viewing them as a multiobjective optimization problem. Every equation in the system represents an objective function whose goal is to minimize the difference between the right and left terms of the corresponding equation. An evolutionary computation technique is applied to solve the problem obtained by transforming the system into a multiobjective optimization problem. The results obtained are compared with a very new technique that is considered as efficient and is also compared with some of the standard techniques that are used for solving nonlinear equations systems. Several wellknown and difficult applications (such as interval arithmetic benchmark, kinematic application, neuropsychology application, combustion application, and chemical equilibrium application) are considered for testing the performance of the new approach. Empirical results reveal that the proposed approach is able to deal with highdimensional equations systems. Index Terms—Computational intelligence, evolutionary multiobjective optimization, metaheuristics, nonlinear equation systems. I.
SOLVING SYSTEMS OF NONLINEAR EQUATIONS WITH CONTINUOUS GRASP
"... ABSTRACT. A method for finding all roots of a system of nonlinear equations is described. Our method makes use of CGRASP, a recently proposed continuous global optimization heuristic. Given a nonlinear system, we solve a corresponding adaptively modified global optimization problem multiple times, ..."
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Cited by 3 (1 self)
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ABSTRACT. A method for finding all roots of a system of nonlinear equations is described. Our method makes use of CGRASP, a recently proposed continuous global optimization heuristic. Given a nonlinear system, we solve a corresponding adaptively modified global optimization problem multiple times, each time using CGRASP, with areas of repulsion around roots that have already been found. The heuristic makes no use of derivative information. We illustrate the approach on systems from the literature. 1.
Improved Estimation of defocus blur and spatial shifts in spatial domain: A homotopybased approach
 Pattern Recognition
"... 1Département de mathématiques ..."
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, 2010
"... Solving structured nonlinear leastsquares and nonlinear feasibility problems ..."
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Solving structured nonlinear leastsquares and nonlinear feasibility problems
SOLVING POLYNOMIAL SYSTEMS USING A MODIFIED LINE SEARCH APPROACH
, 2010
"... Abstract. This paper proposes a modified line search technique for solving systems of complex nonlinear equations. Line search is a widely used iterative global search method. Since optimization strategies have been (and continue to be) successfully used for solving systems of nonlinear equations, t ..."
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Abstract. This paper proposes a modified line search technique for solving systems of complex nonlinear equations. Line search is a widely used iterative global search method. Since optimization strategies have been (and continue to be) successfully used for solving systems of nonlinear equations, the system is reduced to a onedimensional equation system for optimization purpose. The proposed line search procedure incorporates a restart technique, which makes use of derivatives to reduce the search space and to regenerate thereafter the starting points in between the new ranges. Several well known applications such as interval arithmetic benchmark, kinematics, neuropsychology, combustion, chemical equilibrium and economics application are considered for testing the performances of the proposed approach. To validate the strength of the proposed approach, systems having between 5 and 20 equations are considered. Results are compared with an evolutionary algorithm approach, which transforms the problem into a multiobjective optimization problem. Empirical results reveal that the proposed approach is able to deal with high dimensional equations systems very effectively. 1. Introduction. Polynomial
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, 2002
"... Globally convergent inexact quasiNewton methods for solving nonlinear systems ..."
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Globally convergent inexact quasiNewton methods for solving nonlinear systems
Solving Systems of Nonlinear Equations by Harmony Search
"... In this paper, we aim to analyze the performance of some variants of the harmony search (HS) metaheuristic when solving systems of nonlinear equations through the global optimization of an appropriate merit function. The HS metaheuristic draws its inspiration from an artistic process, the improvisat ..."
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In this paper, we aim to analyze the performance of some variants of the harmony search (HS) metaheuristic when solving systems of nonlinear equations through the global optimization of an appropriate merit function. The HS metaheuristic draws its inspiration from an artistic process, the improvisation process of musicians seeking a wonderful harmony. A new differential best HS algorithm, based on an improvisation operator that mimics the best harmony and uses a differential variation, is proposed. Computational experiments involving a wellknown set of smalldimensional problems are presented. Key words: nonlinear equations, metaheuristic, harmony search 1
DOI: 10.1177/1081286512467563
, 2012
"... On the brachistochronic motion of a variablemass mechanical system in general force fields ..."
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On the brachistochronic motion of a variablemass mechanical system in general force fields