An auxiliary function method for constrained systems of nonlinear equations

In this paper, we propose an auxiliary function method to solve constrained systems of nonlinear equations. By introducing an auxiliary function, an unconstrained (box-constrained) optimization problem is constructed for a given constrained system of nonlinear equations. It is shown that any local minimizer of the constructed unconstrained optimization problem is an approximate solution to the given constrained system when parameters are appropriately chosen, and the precision for approximation can be preset. It is also shown that any accumulation point of the local minimizers of the constructed unconstrained optimization problems with a sequence of parameters tending to zero is a solution to the given constrained system of nonlinear equations.