This paper presents a strategy for choosing the initial point, slacks and multipliers in interior methods for nonlinear programming. It consists of first computing a Newton-like step to estimate the magnitude of these three variables and then shifting the slacks and multipliers so that they are sufficiently positive. The new strategy has the option of respecting the initial estimate of the solution given by the user, and attempts to avoid the introduction of artificial non-convexities. Numerical experiments on a large test set illustrate the performance of the strategy.
Report OTC 2003/04, Optimization Technology Center, Northwestern University, May 2003