  We apply novel inner-iteration preconditioned Krylov subspace methods to the
interior-point algorithm for linear programming (LP). Inner-iteration
preconditioners recently proposed by Morikuni and Hayami enable us to overcome
the severe ill-conditioning of linear equations solved in the final phase of
interior-point iterations. The Krylov subspace methods do not suffer from
rank-deficiency and therefore no preprocessing is necessary even if rows of the
constraint matrix are not linearly independent. By means of these methods, a
new interior-point recurrence is proposed in order to omit one matrix-vector
product at each step. Extensive numerical experiments are conducted over
diverse instances of 138 LP problems including the Netlib, QAPLIB, Mittelmann
and Atomizer Basis Pursuit collections. The largest problem has 434,580
unknowns. It turns out that our implementation is more robust than the standard
public domain solvers SeDuMi (Self-Dual Minimization), SDPT3 (Semidefinite
Programming Toh-Todd-T\"ut\"unc\"u) and the LSMR iterative solver in PDCO
(Primal-Dual Barrier Method for Convex Objectives) without increasing CPU time.
The proposed interior-point method based on iterative solvers succeeds in
solving a fairly large number of LP instances from benchmark libraries under
the standard stopping criteria. The work also presents a fairly extensive
benchmark test for several renowned solvers including direct and iterative
solvers.
