Effects of finite-precision arithmetic on interior-point methods for nonlinear programming. (English) Zbl 0994.90139

Wright, Stephen J.

SIAM J. Optim. 12, No. 1, 36-78 (2001).

The stability of primal-dual interior point methods w.r.t. rounding is studied in detail. A major contribution is due to the fact that instead of the usual requirement of strict complementarity and linear independence constraint qualification the relaxed Mangasarian-Fromovitz Constraint Qualification (MFCQ) is considered throughout the paper. Together with the assumed existence of a set of positive multipliers for all active constraints singular value decomposition is applied to derive the stability results. In detail the effects of errors in the occurring numerical subprocesses is taken into consideration. The obtained theoretical results are validate by a simple two-dimensional example which satisfies MFCQ only.

Reviewer: Christian Grossmann (Dresden)

MSC:

90C51	Interior-point methods
90C33	Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
90C30	Nonlinear programming

Keywords:

primal-dual interior point methods; finite-precision arithmetic; nonlinear programming; constraint qualification

Software:

mctoolbox; PCx