Basis partition of the space of linear programs through a differential equation

Gongyun Zhao(matzgynus.edu.sg)

Abstract: The space of linear programs (LP) can be partitioned into a finite number of sets, each corresponding to a basis. This partition is thus called the basis partition. The closed-form solution on the space of LP can be determined with the basis partition if we can characterize the basis partition. A differential equation on the Grassmann manifold which represents the space of LP provides a powerful tool for characterizing the basis partition. In paper [3], the author presented some basic concepts and properties of this differential equation. This paper continues the research of [3] and presents three useful properties.

Keywords: Linear programming, Space of linear programs, Basis partition, Grassmannian/Grassmann manifold, Projection matrix, Differential equation.

Category 1: Linear, Cone and Semidefinite Programming (Linear Programming )

Category 2: Other Topics (Other )

Citation: Research report, National University of Singapore, June 2008

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Entry Submitted: 06/22/2008
Entry Accepted: 06/23/2008
Entry Last Modified: 06/22/2008

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