2018/10/10 by Zhize Li, Wei Zhang, Li, Zhize +2
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #Complexity and Algorithms in Graphs #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1810.04517
openalex publication_date 2018/10/10 · openalex created_date 2018/10/26 · openalex updated_date 2026/07/28
Traditionally, there are several polynomial algorithms for linear programming including the ellipsoid method, the interior point method and other variants. Recently, Chubanov [Chubanov, 2015] proposed a projection and rescaling algorithm, which has become a potentially practical class of polynomial algorithms for linear feasibility problems and also for the general linear programming. However, the Chubanov-type algorithms usually perform much better on the infeasible instances than on the feasible instances in practice. To explain this phenomenon, we derive a new theoretical complexity bound for the infeasible instances based on the condition number, which shows that algorithms can indeed run much faster on infeasible instances in certain situations. In order to speed up the feasible instances, we propose a Polynomial-time Primal-Dual Projection algorithm (called PPDP) by explicitly developing the dual algorithm. The numerical results validate that our PPDP algorithm achieves a quite balanced performance between feasible and infeasible instances, and its performance is remarkably better than previous algorithms.