A ROBUST INTERIOR POINT METHOD FOR COMPUTING THE ANALYTIC CENTER OF AN ILL-CONDITIONED POLYTOPE WITH ERRORS

• 来源期刊: 计算数学（英文版）
• 关键词: Analytic center Ill-conditioning Unboundedness Primal-dual interior point algorithm Convergence Polynomial complexity
• 年，卷（期）: 2019,（6）
• 页码范围: 843-865
• 页数: 23页
• 语种: 英文
• DOI: 10.4208/jcm.1907-m2019-0016

摘要

In this paper we propose an efficient and robust method for computing the analytic center of the polyhedral set P ={x ∈ Rn | Ax =b,x ≥ 0},where the matrix A ∈ Rm×n is ill-conditioned,and there are errors in A and b.Besides overcoming the difficulties caused by ill-conditioning of the matrix A and errors in A and b,our method can also detect the infeasibility and the unboundedness of the polyhedral set P automatically during the computation.Detailed mathematical analyses for our method are presented and the worst case complexity of the algorithm is also given.Finally some numerical results are presented to show the robustness and effectiveness of the new method.