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Original scientific paper

A new projection-based algorithm for solving a large-scale nonlinear system of monotone equations

Mushtak A. K. Shiker ; University of Babylon, Babylon, Iraq
Keyvan Amini ; Faculty of Science, Razi University, Kermanshah, Iran

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page 63-73

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Projection-based methods are an efficient and applicable family of derivative free methods for solving nonlinear monotone systems. This paper proposes a new projection method for solving a system of large-scale nonlinear monotone equations. The new algorithm, in each iteration, by using a modified conjugate gradient direction, constructs an appropriate hyperplane that strictly separates the current approximation from the solution set of the problem. Then the new approximation is determined by projecting the current point onto the separating hyperplane. The global convergence and the linear convergence rate of the proposed algorithm are proved under standard assumptions. Preliminary numerical experiments indicate that the proposed algorithm is promising.


projection method, nonlinear system, monotone equations, conjugate gradient direction, global convergence

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