Solving nonlinear systems of equations with simple constraints (Q1384164)

For continuously differentiable \(F:\mathbb{R}^n\to\mathbb{R}^n\) and some closed, convex set \(\Omega\subset\mathbb{R}^n\) consider solving the constrained problem (1) \(F(x)=0\), \(x\in\Omega\). A variant of the inexact Newton method is proposed and, under the assumption of the boundedness of the level set \(\{x\in\Omega: F(x)^TF(x)\leq F(x_0)^TF(x_0)\}\), it is shown that, when the process does not break down, each limit point of the resulting infinite sequence of iterates is a solution of (1). Implementation details for the case of box-constraints \(\{x\in\mathbb{R}^n: \ell\leq x\leq u\}\), \(\ell,u\in\mathbb{R}^n\) are discussed and then a number of numerical examples are given involving nonlinear systems with this type of constraints. Most of these examples concern the computation of singular points on solution paths of homotopies.