A new nonmonotone smoothing Newton method for the symmetric cone complementarity problem with the Cartesian $$P_0$$ P 0 -property

Xiangjing Liu () and Sanyang Liu ()
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Xiangjing Liu: Xidian University
Sanyang Liu: Xidian University

Mathematical Methods of Operations Research, 2020, vol. 92, issue 2, No 1, 229-247

Abstract: Abstract We present a new smoothing Newton method for the symmetric cone complementarity problem with the Cartesian $$P_0$$ P 0 -property. The new method is based on a new smoothing function and a nonmonotone line search which contains a monotone line search as a special case. It is proved that the new method is globally and locally superlinearly/quadratically convergent under mild conditions. Preliminary numerical results are also reported which indicate the proposed method is promising.

Keywords: Smoothing Newton method; Symmetric cone; Complementarity problem; Cartesian $$P_0$$ P 0 -property; 90C33; 65K05 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s00186-020-00709-7

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