Abstract:

It is well known that a large neighborhood interior point algorithm for linear optimization performs much better in implementation than its small neighborhood counterparts. One of the key elements of interior point algorithms is how to update the barrier parameter. The main goal of this paper is to introduce an "adaptive'' long step interior-point algorithm in a large neighborhood of central path using the classical logarithmic barrier function having $O(n\log\frac{(x^0)^Ts^0}{\epsilon})$ iteration complexity analogous to the classical long step algorithms. Preliminary encouraging numerical results are reported.