Ill-Conditioning and Computational Error in Interior Methods for Nonlinear Programming

Margaret H. Wright

Ill-conditioning has long been regarded as a plague on interior methods for nonlinear programming, but its damaging effects have rarely been documented. We offer some insight into this seeming contradiction by analyzing ill-conditioning in a primal-dual method. (A similar analysis applies to the primal barrier method.) Our conclusion is that in most instances ill-conditioning does not noticeably impair the accuracy of the solution.

Technical Report 97-4-04, Computing Sciences Research Bell Laboratories, Murray Hill, New Jersey April 25, 1997