Abstract
In this paper, we consider a primal-dual Newton method for linear complementarity problems (LCP) with P *(κ)-matrix. By using some new analysis tools, we prove polynomial complexity of the large update method without using a barrier or potential function. Our analysis is based on an appropriate proximity measure only. This proximity measure has not been used in the analysis of a large update method for LCP before. Our new analysis provides a unified way to analyze both large update and small update methods. The polynomial complexity of the method of finding a maximally complementarity solution is discussed as well.
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Peng, J., Roos, C., Terlaky, T. (2000). New Complexity Analysis of Primal-Dual Newton Methods for P *(κ) Linear Complementarity Problems. In: Frenk, H., Roos, K., Terlaky, T., Zhang, S. (eds) High Performance Optimization. Applied Optimization, vol 33. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3216-0_10
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DOI: https://doi.org/10.1007/978-1-4757-3216-0_10
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