Gongyun Zhao – Optimization Online

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

Published: 2008/06/22, Updated: 2022/05/13

Linear Programming, Other Topics basis partition, differential equation, grassmannian/grassmann manifold, linear programming, projection matrix, space of linear programs

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 … Read more

Representing the space of linear programs as a Grassmannian

Published: 2006/03/03

Gongyun Zhao

Linear, Cone and Semidefinite Programming grassmannian/grassmann manifold, linear programming, projection matrix, space of linear programs

We represent the space of linear programs as the space of projection matrices. Projection matrices of the same dimension and rank comprise a Grassmannian, which has rich geometric and algebraic structures. An ordinary differential equation on the space of projection matrices defines a path for each projection matrix associated with a linear programming instance and … Read more