An infeasible-interior-point potential-reduction algorithm for linear programming |
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| Authors: | Tütüncü Reha H. |
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| Affiliation: | (1) Department of Mathematics and Computer Science, Shimane University, Matsue 690-8504, Japan, e-mail: chen@math.shimane-u.ac.jp. Some of this work was supported by the Australian Research Council., JP;(2) Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan, e-mail: fuku@kuamp.kyoto-u.ac.jp. This author’s work was supported in part by the Scientific Research Grant-in-Aid from the Ministry of Education, Science and Culture, Japan., JP |
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| Abstract: | ![]()
n . The method is based on Rockafellar’s proximal point algorithm and a cutting-plane technique. At each step, we use an approximate proximal point pa(xk) of xk to define a vk∈∂εkf(pa(xk)) with εk≤α∥vk∥, where α is a constant. The method monitors the reduction in the value of ∥vk∥ to identify when a line search on f should be used. The quasi-Newton step is used to reduce the value of ∥vk∥. Without the differentiability of f, the method converges globally and the rate of convergence is Q-linear. Superlinear convergence is also discussed to extend the characterization result of Dennis and Moré. Numerical results show the good performance of the method. Received October 3, 1995 / Revised version received August 20, 1998 Published online January 20, 1999 |
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| Keywords: | : nondifferentiable convex optimization – proximal point – quasi-Newton method – cutting-plane method – bundle methods Mathematics Subject Classification (1991): 65K05, 90C30 |
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