In this paper, a new trust-region subproblem combining with the BFGS update is proposed for solving nonlinear equations, where the trust region radius is defined by a new way. The global convergence without the nondegeneracy assumption and the quadratic convergence are obtained under suitable conditions. Numerical results show that this method is more effective than the norm method.

A BFGS trust-region method for nonlinear equations

In this article, we propose a BFGS method for solving symmetric nonlinear equations. The presented method possesses some favourable properties: (a) the generated sequence of iterates is norm descent; (b) the generated sequence of the quasi-Newton matrix is positive definite and (c) this method possesses the global convergence and superlinear convergence. Numerical results show that the presented method is interesting.

A BFGS algorithm for solving symmetric nonlinear equations

A trust-region-based BFGS method is proposed for solving symmetric
nonlinear equations. In this given algorithm, if the trial step is unsuccessful, the
linesearch technique will be used instead of repeatedly solving the subproblem of the
normal trust-region method. We establish the global and superlinear convergence
of the method under suitable conditions. Numerical results show that the given
method is competitive to the normal trust region method.

/pdf/a-trust-region-based-bfgs-method-with-line-search-technique-18h0gdvcdh.pdf

A Trust-Region-Based BFGS Method with Line Search Technique for Symmetric Nonlinear Equations

In this article, a new method is proposed for solving symmetric nonlinear equations, which can ensure that the search direction is descent for the norm function without carrying any line search technique. Under mild conditions, the global convergence of the given method is established. Numerical results show that the proposed method is effective for the given test problems.

A New Method with Descent Property for Symmetric Nonlinear Equations

In this paper, a Gauss-Newton-based Broyden’s class method for parameters of regression problems is presented. The global convergence of this given method will be established under suitable conditions. Numerical results show that the proposed method is interesting.

/pdf/a-gauss-newton-based-broyden-s-class-algorithm-for-569cpz5w5w.pdf

A Gauss-Newton-Based Broyden’s Class Algorithm for Parameters of Regression Analysis

In this paper, a rank-one updated method for solving symmetric nonlinear equations is proposed. This method possesses some features: 1) The updated matrix is positive definite whatever line search technique is used; 2) The search direction is descent for the norm function; 3) The global convergence of the given method is established under reasonable conditions. Numerical results show that the presented method is interesting.

/pdf/a-rank-one-fitting-method-with-descent-direction-for-solving-27zp5bikb1.pdf

Gonglin Yuan

Papers

A Rank-One Fitting Method with Descent Direction for Solving Symmetric Nonlinear Equations