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

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

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