Abstract
This paper considers the linear weighted complementarity problem (denoted by LWCP) introduced by Potra (SIAM J Optim 22:1634–1654, 2012). Based on two weighted smoothing functions, we propose a new nonmonotone smoothing algorithm for solving the LWCP and establish its global and local quadratic convergence without the strict complementarity assumption. Compared to existing nonmonotone smoothing algorithms, the proposed algorithm solves the linear system only approximately which can save the computation work when one solves large-scale LWCPs. Moreover, the nonmonotone line search technique adopted in this paper includes the usual monotone line search and some existing nonmonotone line searches as special cases. Numerical results show that our algorithm is considerably efficient for solving large-scale LWCPs.
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Acknowledgements
Research of this paper was partly supported by National Natural Science Foundation of China (11371306, 11601466), Basic and Frontier Technology Research Project of Henan Province (162300410071) and Nanhu Scholars Program for Young Scholars of XYNU. We are very grateful to referees for their valuable suggestions which have considerably improved the paper.
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Communicated by Joerg Fliege.
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Tang, J. A variant nonmonotone smoothing algorithm with improved numerical results for large-scale LWCPs. Comp. Appl. Math. 37, 3927–3936 (2018). https://doi.org/10.1007/s40314-017-0554-6
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DOI: https://doi.org/10.1007/s40314-017-0554-6
Keywords
- Linear weighted complementarity problem
- Smoothing algorithm
- Inexact Newton method
- Nonmonotone line search