Sphere Methods for LP


  • Katta G. Murty University of Michigan
  • Mohammad R. Oskoorouchi California State University San Marcos


Linear Programming (LP), Interior point methods (IPMs), Large scale LPs, Ball centers of polytopes, Solving LPs using matrix inversions sparingly.


The sphere method for solving linear programs operates with only a subset of constraints in the model in each iteration, and thus has the advantage of handling instances which may not be very sparse. In this paper we discuss enhancements, and improved versions Sphere Methods 2, 2.1 which improve performance by 20 to 80%. Additional steps that can improve performance even more are also presented.

Author Biographies

Katta G. Murty, University of Michigan

Professor, Industrial and Operations Engineering Department, University of Michigan, Ann Arbor, MI-48109-2117, USA.

Mohammad R. Oskoorouchi, California State University San Marcos

Department of Information Systems and Operations Management, College of Business Administration, California State University San Marcos, San Marcos, CA 92096-0001, USA,




How to Cite

Murty, K. G., & Oskoorouchi, M. R. (2010). Sphere Methods for LP. Algorithmic Operations Research, 5(1), Pages 21 – 33. Retrieved from https://journals.lib.unb.ca/index.php/AOR/article/view/11168