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Feasibility control in nonlinear optimization. (English) Zbl 0978.65050

DeVore, Ronald A. (ed.) et al., Foundations of computational mathematics. Conference, Oxford, GB, July 18-28, 1999. Cambridge: Cambridge University Press. Lond. Math. Soc. Lect. Note Ser. 284, 125-154 (2001).
Summary: 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 systems of nonlinear equations and equality constrained optimization, as well as in interior-point methods for nonlinear programming.
For the entire collection see [Zbl 0962.00005].

MSC:

65K05 Numerical mathematical programming methods
90C30 Nonlinear programming
90C51 Interior-point methods
90C53 Methods of quasi-Newton type
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