Perturbed Newton Method with Trust-region Time-stepping Schemes for Linear Programming with Uncertain Data
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In this article, we consider the path-following method based on the perturbed Newton flow with the new trust-region time-stepping scheme for the standard linear programming problem. For the problem with deficient rank matrix and the noise right-hand-side vector, we also give the pre-processing method based on the singular value decomposition. Then, we analyze the global convergence of the new method when the initial point is strictly primal-dual feasible. Finally, we test the new method for some problems with deficient rank matrices, and compare it with other popular interior-point methods such as the path-following method (the subroutine pathfollow.m coded by M. C. Ferris <cit.>) and Mehrotra's predictor-corrector algorithm (the built-in subroutine linprog.m of the MATLAB environment, which was implemented by S. Mehrotra and Y. Zhang <cit.>). Numerical results show that the new method is more robust than those methods for the large-scale deficient-rank problems without sacrificing its computational efficiency.
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