Solving convex (and linear) complementarity problems by projection methods (undamped Newton)
A recent approach for solving the Linear Complementarity Problem (LCP) has been the solution of an equivalent system of piecewise linear equations through damped Newton methods. Since these functions are not everywhere differentiable, Newton methods have been adapted to deal with B-differentiable functions. The main drawback of this approach is the need to globalize the results by means of a step-size procedure. We adapt a new method of projections on certain convex sets to solve the LCP. This approach becomes a Newton method with no need of stepsize. Both the theoretical and practical implications are encouraging. The convergence conditions extend with no modifications to a more general convex complementarity problem. If the procedure converges to a nondegenerate solution, the usual Newton quadratic rate of convergence is achieved.
- OSTI ID:
- 36050
- Report Number(s):
- CONF-9408161--
- Country of Publication:
- United States
- Language:
- English
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