Geodesic
A smoothing Levenberg-Marquardt method for the complementarity problem over symmetric cone
Applications of Mathematics, Tome 67 (2022) no. 1, pp. 49-64.

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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.
DOI : 10.21136/AM.2021.0064-20
Classification : 65K05, 65K10, 90C33
Keywords: complementarity problem; symmetric cone; Levenberg-Marquardt method; Euclidean Jordan algebra; local error bound 
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     title = {A smoothing {Levenberg-Marquardt} method for the complementarity problem over symmetric cone},
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Liu, Xiangjing; Liu, Sanyang. A smoothing Levenberg-Marquardt method for the complementarity problem over symmetric cone. Applications of Mathematics, Tome 67 (2022) no. 1, pp. 49-64. doi : 10.21136/AM.2021.0064-20. http://geodesic.mathdoc.fr/articles/10.21136/AM.2021.0064-20/

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