Interior Point Methods for Network Problems (An Efficient Conjugate Gradient Method for Interior Point Methods)

네트워크 문제에서 내부점 방법의 활용 (내부점 선형계획법에서 효율적인 공액경사법)

Cholesky factorization is known to be inefficient to problems with dense column and network problems in interior point methods. We use the conjugate gradient method and preconditioners to improve the convergence rate of the conjugate gradient method. Several preconditioners were applied to LPABO 5.1 and the results were compared with those of CPLEX 3.0. The conjugate gradient method shows to be more efficient than Cholesky factorization to problems with dense columns and network problems. The incomplete Cholesky factorization preconditioner shows to be the most efficient among the preconditioners.