We analyze the properties that optimization algorithms must possess in order to prevent convergence to non-stationary points for the merit function. We show that demanding the exact satisfaction of constraint linearizations results in di culties in a wide range of optimization algorithms. Feasibility control is a mechanism that prevents convergence to spurious solutions by ensuring that su cient progress towards feasibility is made, even in the presence of certain rank de ciencies. The concept

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... f feasibility control is studied in this paper in the context of Newton methods for nonlinear systems of equations and equality constrained optimization, as well as in interior methods for nonlinear programming.