A new polynomial-time algorithm for linear programming
Combinatorica
Multiple centrality corrections in a primal-dual method for linear programming
Computational Optimization and Applications
On the simplex algorithm 'revised form'
Advances in Engineering Software
A new efficient primal dual simplex algorithm
Computers and Operations Research
Scaling linear optimization problems prior to application of the simplex method
Computational Optimization and Applications
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One of the most significant and well-studied optimization problems is the Linear Programming problem (LP). Many algorithms have been proposed for the solution of Linear Programming problems (LPs); the main categories of them are: (i) simplex-type or pivoting algorithms, (ii) interior-point methods (IPM) and (iii) exterior point simplex type algorithms (EPSA). Prior to the application of these algorithms, some preconditioning techniques are executed in order to improve the computational properties of LPs. Scaling is the most widely used preconditioning technique and is used to reduce the condition number of the constraint matrix, reduce the number of iterations required to solve LPs and improve the numerical behavior of the algorithms. The aim of this paper is to present a computational study of the impact of scaling prior to the application of the aforementioned algorithms. In the computational study that we have conducted, we calculate both the CPU time and the number of iterations with and without scaling for a set of sparse randomly generated optimal LPs. The scaling techniques that we applied to the above mentioned algorithms are: (i) arithmetic mean, (ii) equilibration, and (iii) geometric mean scaling techniques. Computational results showed that equilibration is the best scaling technique and that the effect of scaling is significant to IPM and revised simplex algorithm, while EPSA is scaling invariant.