Abstract
In the predictor-corrector method of Mizuno, Todd and Ye [1], the duality gap is reduced only at the predictor step and is kept unchanged during the corrector step. In this paper, we modify the corrector step so that the duality gap is reduced by a constant fraction, while the predictor step remains unchanged. It is shown that this modified predictor-corrector method retains the\(O(\sqrt n L)\) iteration complexity as well as the local quadratic convergence property.
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References
S. Mizuno, M.J. Todd, and Y. Ye, “On adaptive-step primal-dual interior-point algorithms for linear programming,” Technical Report No. 944, School of Operations Research and Industrial Engineering, Cornell University, (Ithaca, New York), 1990, to appear in Math. Oper. Res.
R.C. Monteiro and I. Adler, “Interior path following primal-dual algorithms: Part I, Linear Programming,” Department of IEOR, University of California, Berkeley, CA, 1987.
Y. Ye and K.M. Anstreicher, “On quadratic and\(O(\sqrt n L)\) convergence of a predictor-corrector algorithm for LCP,” Working Paper No. 91-20, The College of Business Administration, The University of Iowa, Iowa City, IA, 1991, to appear in Math. Prog.
Y. Ye, O. Güler, R.A. Tapia, and Y. Zhang, “A quadratically convergent\(O(\sqrt n L)\)-interation algorithm for linear programming,” Working Paper No 91-14, The College of Business Administration, The University of Iowa, Iowa City, IA, 1991, also TR91-26, Department of Mathematical Sciences, Rice University, Houston, TX, 1991, to appear in Math. Prog.
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Luo, ZQ., Wu, S. A modified predictor-corrector method for linear programming. Comput Optim Applic 3, 83–91 (1994). https://doi.org/10.1007/BF01299392
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DOI: https://doi.org/10.1007/BF01299392