  


A Bound for the Number of Different Basic Solutions Generated by the Simplex Method
Tomonari Kitahara (kitahara.t.abm.titech.ac.jp) Abstract: In this short paper, we give an upper bound for the number of different basic feasible solutions generated by the simplex method for linear programming problems having optimal solutions. The bound is polynomial of the number of constraints, the number of variables, and the ratio between the minimum and the maximum values of all the positive elements of primal basic feasible solutions. When the primal problem is nondegenerate, it becomes a bound for the number of iterations. We show some basic results when it is applied to special linear programming problems. The results include strongly polynomiality of the simplex method for Markov Decision Problem by Ye and utilize its analysis. Keywords: Simplex method, Linear programming, Iteration bound, Category 1: Linear, Cone and Semidefinite Programming (Linear Programming ) Citation: To appear in Mathematical Programming Download: Entry Submitted: 01/19/2011 Modify/Update this entry  
Visitors  Authors  More about us  Links  
Subscribe, Unsubscribe Digest Archive Search, Browse the Repository

Submit Update Policies 
Coordinator's Board Classification Scheme Credits Give us feedback 
Optimization Journals, Sites, Societies  