On Efficiency of Non-Monotone Adaptive Trust Region and Scaled Trust Region Methods in Solving Nonlinear Systems of Equations

A Non-monotone Adaptive Trust Region Algorithm For Nonlinear Equations

In this paper, a non-monotone adaptive trust region method for the system of non-linear equations is proposed, in part, which is based on the technique in [9]. The local and global convergence properties of non-monotone adaptive trust region method are proved under favorable conditions. Some numerical experiments show that the method is effective.

A Trust Region Algorithm for Solving Nonlinear Equations (RESEARCH NOTE)

This paper presents a practical and efficient method to solve large-scale nonlinear equations. The global convergence of this new trust region algorithm is verified. The algorithm is then used to solve the nonlinear equations arising in an Expanded Lagrangian Function (ELF). Numerical results for the implementation of some large-scale problems indicate that the algorithm is efficient for these ...

Trust-region methods for rectangular systems of nonlinear equations

Here Θ : X → IR is a continuously differentiable mapping, X ⊆ IR is an open set containing the feasible region Ω and Ω is an n-dimensional box, Ω = {x ∈ IR : l ≤ x ≤ u}. These inequalities are meant component-wise and l ∈ (IR ∪−∞), u ∈ (IR ∪∞). Taking into account the variety of applications yielding the problem (1), we allow any relationship between m and n. The relevance of this problem is we...

A Trust Region Algorithm for Solving Nonlinear Equations

This paper presents a practical and efficient method to solve large-scale nonlinear equations. The global convergence of this new trust region algorithm is verified. The algorithm is then used to solve the nonlinear equations arising in an Expanded Lagrangian Function (ELF). Numerical results for the implementation of some large-scale problems indicate that the algorithm is efficient for these ...

A Non - monotone Trust - Region Filter Algorithm

Combining filter and non-monotone trust region algorithm for nonlinear systems of equalities and inequalities

In this paper, we combine filter and non-monotone trust region algorithm for nonlinear systems of equalities and inequalities. The systems of equalities and inequalities are transformed into a continuous equality constrained optimization solved by the new algorithm. Filter method guarantees global convergence of the algorithm under appropriate assumptions. The second order correction step is us...