Patent ID: 8359286

Claim:
A method of optimizing a linear optimization problem subject to a change of constraints, said method comprising: determining a first set of constraints for said linear optimization problem; initializing the optimization problem into an initial feasible format to be operated on by the computer; initiating processing by a computer to optimize said optimization problem in accordance with said first set of constraints; determining a second set of constraints different from said first set of constraints; continuing processing with said computer to optimize said optimization problem by using said second set of constraints in place of said first set of constraints without having to re-initialize the optimization problem into another initial feasible format; wherein said optimization problem has “m” constraints and wherein said determining said first set of constraints for said linear optimization problem comprises: determining if said constraint(s) contain any inequalities; determining if said constraint(s) contain any equalities; modifying each of said equality constraint(s) by adding a different artificial variable to each of said equality constraint(s); converting each of said inequality constraint(s) by adding a different canonical variable to each of said inequality constraint(s) so as to make each inequality constraint an equality; wherein the constraints j=1 n a ij x j +y i =b i with y i 0 for i=1, . . . , m and with each y i being a slack variable satisfy the relationship [A][X]+[I][Y]=[B], wherein [A] is a matrix having m rows and n columns and contains the values a ij for i=1, . . . , m and for j=1, . . . , n and represents the coefficients for the variables in matrix [X], wherein [X] is a matrix having n rows and one column and storing the values x j for j=1, . . . , n, wherein [Y] is a matrix having m rows and one column and represents the variables y i for i=1 to m and wherein [B] is a matrix having m rows and one column and represents a matrix of numbers b j for i=1, . . . , m, and wherein [I] is an identity matrix having m rows and m columns.