"Feasibility Control in Nonlinear Optimization "
M. Marazzi, J. Nocedal
''Foundations of Computational Mathematics'', eds. A DeVore, A. Iserles, E. Suli
London Mathematical Society Lecture Notes; Series 284, pp. 125-154,
Cambridge University Press (2001)
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 difficulties in a wide range of optimization algorithms. Feasibility control is a mechanism that prevents convergence to spurious solutions by ensuring that sufficient progress towards feasibility is made, even in the presence of certain rank deficiencies. The concept of 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.