Abstract: To solve constrained nonlinear equations based on optimization
algorithms is suffered a difficulty that the authors obtain just a stationary point or a local minimizer of the underlying optimization problem, which is not necessarily a solution of the equations. Then the arising problem is how to get a better point from the stationary point or the local minimizer point. By using a projection-type method, this paper extends the Lagrangian globalization (LG) method [8, 9] to a system of
nonlinear equations with bounded constraints. The authors prove that from a stationary point, the LG projection method can find a better point. Numerical examples also show that the LG method has a potential to escape the stationary point of optimization problems.

Key words: Constrained equations, Lagrangian globalization method, Stationary point, Global convergence