On the formulation and theory of the Newton interior-point method for nonlinear programming |
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| Authors: | A S El-Bakry R A Tapia T Tsuchiya Y Zhang |
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| Institution: | (1) Department of Mathematics, Faculty of Science, Alexandria University, Alexandria, Egypt;(2) Center for Research on Parallel Computations, Rice University, Houston, Texas;(3) Department of Computational and Applied Mathematics, Rice University, Houston, Texas;(4) Department of Prediction and Control, Institute of Statistical Mathematics, Minami-Azabu, Minato-Ku, Tokyo, Japan;(5) Department of Mathematics and Statistics, University of Maryland Baltimore County, Baltimore, Maryland |
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| Abstract: | In this work, we first study in detail the formulation of the primal-dual interior-point method for linear programming. We show that, contrary to popular belief, it cannot be viewed as a damped Newton method applied to the Karush-Kuhn-Tucker conditions for the logarithmic barrier function problem. Next, we extend the formulation to general nonlinear programming, and then validate this extension by demonstrating that this algorithm can be implemented so that it is locally and Q-quadratically convergent under only the standard Newton method assumptions. We also establish a global convergence theory for this algorithm and include promising numerical experimentation.The first two authors were supported in part by NSF Cooperative Agreement No. CCR-8809615, by Grants AFOSR 89-0363, DOE DEFG05-86ER25017, ARO 9DAAL03-90-G-0093, and the REDI Foundation. The fourth author was supported in part by NSF DMS-9102761 and DOE DE-FG02-93ER25171. The authors would like to thank Sandra Santos for painstakingly proofreading an earlier verion of this paper. |
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| Keywords: | Interior-point methods primal-dual methods nonlinear programming superlinear and quadratic convergence global convergence |
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