Dual versus primal-dual interior-point methods for linear and conic programming

We observe a curious property of dual versus primal-dual path-following interior-point methods when applied to unbounded linear or conic programming problems in dual form. While primal-dual methods can be viewed as implicitly following a central path to detect primal infeasibility and dual unboundedness, dual methods can sometimes implicitly move away from the analytic center of the set of infeasibility/unboundedness detectors. Dedicated to Clovis Gonzaga on his 60th birthday. ∗School of Operations Research and Industrial Engineering, Cornell University, Ithaca, New York 14853, USA ([email protected]). This author was supported in part by NSF through grant DMS-0209457 and ONR through grant N00014-02-1-0057.