Abstract
In this paper, we propose a quasi-Newton method for solving systems of monotone equations. The method is a combination of the Broyden method and the hyperplane projection method. Under appropriate conditions, we prove that the proposed method is globally convergent. Preliminary numerical results show that the proposed method is promising.
Highlights
IntroductionWe consider the problem of finding a solution of the nonlinear system of equations
In this paper, based on the hyperplane projection method [10], we propose a quasiNewton method for solving systems of monotone equations without use of merit functions
We show that the proposed method is globally convergent
Summary
We consider the problem of finding a solution of the nonlinear system of equations. Solodov and Svaiter [10] presented a Newton-type algorithm for solving systems of monotone equations. Griewank [4] obtained a global convergence results for Broyden’s rank one method. Li, Qi and Zhou [5] generalized the method in [6] and proposed a globally convergent and norm descent BFGS method for solving symmetirc equations. Zhou and Li [13] proposed a global convergence BFGS method for systems of monotone equations without use of merit functions. In this paper, based on the hyperplane projection method [10], we propose a quasiNewton method for solving systems of monotone equations without use of merit functions. 2, after recalling hyperplane projection method, we present the algorithm.
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