A globally optimization algorithm for systems of nonlinear equations
- Authors: Mammadov, Musa , Taheri, Sona
- Date: 2010
- Type: Text , Conference paper
- Relation: Proceedings of PCO 2010, The Third International Conference on Power Control and Optimization 2010 Gold Coast p. 214-234
- Full Text: false
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- Description: In this paper, a new algorithm is proposed for the solutions of system of nonlinear equations. This algorithm uses a combination of the gradient and Newton's methods. A novel dynamic combinator is developed to determine the contribution of the methods in the combination. Also, by using some parameters in the proposed algorithm, this contribution is adjusted. The efficiency of the algoritms is studied in solving system of nonlinear equations.
Solving systems of nonlinear equations using a globally convergent optimization algorithm
- Authors: Taheri, Sona , Mammadov, Musa
- Date: 2012
- Type: Text , Journal article
- Relation: Global Journal of Technology & Optimization Vol. 3, no. (2012), p. 132-138
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- Reviewed:
- Description: Solving systems of nonlinear equations is a relatively complicated problem for which a number of different approaches have been presented. In this paper, a new algorithm is proposed for the solutions of systems of nonlinear equations. This algorithm uses a combination of the gradient and the Newton’s methods. A novel dynamic combinatory is developed to determine the contribution of the methods in the combination. Also, by using some parameters in the proposed algorithm, this contribution is adjusted. We use the gradient method due to its global convergence property, and the Newton’s method to speed up the convergence rate. We consider two different combinations. In the first one, a step length is determined only along the gradient direction. The second one is finding a step length along both the gradient and the Newton’s directions. The performance of the proposed algorithm in comparison to the Newton’s method, the gradient method and an existing combination method is explored on several well known test problems in solving systems of nonlinear equations. The numerical results provide evidence that the proposed combination algorithm is generally more robust and efficient than other mentioned methods on someimportant and difficult problems.