A smoothing Levenberg-Marquardt method for the complementarity problem over symmetric cone

Xiangjing Liu; Sanyang Liu

Applications of Mathematics (2022)

  • Volume: 67, Issue: 1, page 49-64
  • ISSN: 0862-7940

Abstract

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In this paper, we propose a smoothing Levenberg-Marquardt method for the symmetric cone complementarity problem. Based on a smoothing function, we turn this problem into a system of nonlinear equations and then solve the equations by the method proposed. Under the condition of Lipschitz continuity of the Jacobian matrix and local error bound, the new method is proved to be globally convergent and locally superlinearly/quadratically convergent. Numerical experiments are also employed to show that the method is stable and efficient.

How to cite

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Liu, Xiangjing, and Liu, Sanyang. "A smoothing Levenberg-Marquardt method for the complementarity problem over symmetric cone." Applications of Mathematics 67.1 (2022): 49-64. <http://eudml.org/doc/298276>.

@article{Liu2022,
abstract = {In this paper, we propose a smoothing Levenberg-Marquardt method for the symmetric cone complementarity problem. Based on a smoothing function, we turn this problem into a system of nonlinear equations and then solve the equations by the method proposed. Under the condition of Lipschitz continuity of the Jacobian matrix and local error bound, the new method is proved to be globally convergent and locally superlinearly/quadratically convergent. Numerical experiments are also employed to show that the method is stable and efficient.},
author = {Liu, Xiangjing, Liu, Sanyang},
journal = {Applications of Mathematics},
keywords = {complementarity problem; symmetric cone; Levenberg-Marquardt method; Euclidean Jordan algebra; local error bound},
language = {eng},
number = {1},
pages = {49-64},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A smoothing Levenberg-Marquardt method for the complementarity problem over symmetric cone},
url = {http://eudml.org/doc/298276},
volume = {67},
year = {2022},
}

TY - JOUR
AU - Liu, Xiangjing
AU - Liu, Sanyang
TI - A smoothing Levenberg-Marquardt method for the complementarity problem over symmetric cone
JO - Applications of Mathematics
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 67
IS - 1
SP - 49
EP - 64
AB - In this paper, we propose a smoothing Levenberg-Marquardt method for the symmetric cone complementarity problem. Based on a smoothing function, we turn this problem into a system of nonlinear equations and then solve the equations by the method proposed. Under the condition of Lipschitz continuity of the Jacobian matrix and local error bound, the new method is proved to be globally convergent and locally superlinearly/quadratically convergent. Numerical experiments are also employed to show that the method is stable and efficient.
LA - eng
KW - complementarity problem; symmetric cone; Levenberg-Marquardt method; Euclidean Jordan algebra; local error bound
UR - http://eudml.org/doc/298276
ER -

References

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