Interior point path following algorithms
In the last few years the research on interior point methods for linear programming has been dominated by the study of primal-dual algorithms. Most of these methods are easily extended to monotone linear complementarity problems, preserving the convergence properties. In this talk we concentrate mostly on the basic techniques used for following the primal-dual central path associated with a monotone horizontal LCP. The emphasis is on feasible interior point methods, but we also describe the main techniques for dealing with infeasible starting points. We define the central path and construct homotopy methods for following it, with iterations based on the application of Newton`s method. We show how these Newton steps are combinations of two special directions, the affine-scaling and the centering direction, and describe how this fact can be used to generate large step methods with low polynomial bounds and superlinear rates of convergence.
- OSTI ID:
- 36078
- Report Number(s):
- CONF-9408161--
- Country of Publication:
- United States
- Language:
- English
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