The dual simplex method with bounds

• By convention, the vector formed by taking together all the basic variables is denoted xB. Similarly, cB, `B and uB are formed by taking together the same indices of c, ` and u, respectively. The same notation is also used for the indices in L and U , giving cL, cU , `L, `U , uL, and uU . We already defined B as taking together the basic columns of A. The remaining (nonbasic) columns form the submatrices L and U . Thus, there is a permutation of the columns of A that is given by [B | L | U ]. For conciseness, we will write A = [B | L | U ], although it is an abuse of notation.