A Smoothing Newton Algorithm for a Class of Non-monotonic Symmetric Cone Linear Complementarity Problems

Nan Lu and Zheng-Hai Huang ()
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Nan Lu: Xidian University
Zheng-Hai Huang: Tianjin University

Journal of Optimization Theory and Applications, 2014, vol. 161, issue 2, No 6, 446-464

Abstract: Abstract Recently, the study of symmetric cone complementarity problems has been a hot topic in the literature. Many numerical methods have been proposed for solving such a class of problems. Among them, the problems concerned are generally monotonic. In this paper, we consider symmetric cone linear complementarity problems with a class of non-monotonic transformations. A smoothing Newton algorithm is extended to solve this class of non-monotonic symmetric cone linear complementarity problems; and the algorithm is proved to be well-defined. In particular, we show that the algorithm is globally and locally quadratically convergent under mild assumptions. The preliminary numerical results are also reported.

Keywords: Symmetric cone complementarity problem; Euclidean Jordan algebra; Smoothing Newton algorithm; Global convergence; Local quadratic convergence (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10957-013-0436-z

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