Higher Order Methods and their Performance

A class of primal dual interior point methods is developed These methods use a higher order Taylor polynomial to approximate a primal dual trajectory de ned from an infeasible point A detailed implementation of these methods is given and their computational performance is studied We give computational results for two di erent approaches for de ning trajectory and using up to th order polynomial In all cases all the tested netlib problems were solved using default settings The use of higher order polynomial on the average results in approximately to reduction in the number of iterations On several di cult problems in the netlib test set this translates into to savings in cpu time y Supported in part by a grant from the GTE Laboratories and by grants CCR and CCR from the National Science Foundation