Efficiency Attic method

However, since bound constraints are crucial to the efficiency of the Attic method, it is very important that they are assigned for all the variables. 

The fourth significant difference is that some of the matrix J rows may be artificial constraints. This is the real, and most important, difference between Attic and Simplex or Interior Point methods, and makes the Attic method extremely flexible and potentially more efficient than the traditional methods. 

In the Simplex method, a (variable) column is inserted into the basic matrix and another one exits from it at each iteration. The column exchanged can be any column in the existing matrix and this leads to several difficulties in updating the new column in terms of memory allocation and factorization stability as well. In the Attic method, one row is introduced at a time, but it is not inserted between the rows already present. This new row is inserted immediately after the rows already factorized. The factorization of the new row can be efficiently performed by exploiting the existing factorization of the rows already present in the matrix, and the sparsity of both the new and the existing rows. 

Chapter 10 introduces the Attic method for linear programming, and to which we dedicate a complete volume (Vol. 5 - Buzzi-Ferraris and Manenti, in progress) because of the huge significance of the method. The Attic method is compared to the existing Simplex and Interior Point methods, emphasizing its efficiency and robustness. 

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See also in sourсe #XX -- [ ]

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