On the formulation and theory of the Newton interior-point method for nonlinear programming
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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.
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- On the formulation and theory of the Newton interior-point method for nonlinear programming
Journal of Optimization Theory and Applications
Volume 89, Issue 3 , pp 507-541
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers-Plenum Publishers
- Additional Links
- Interior-point methods
- primal-dual methods
- nonlinear programming
- superlinear and quadratic convergence
- global convergence
- Industry Sectors
- Author Affiliations
- 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