A smoothing Newton method for the second-order cone complementarity problem

Jingyong Tang; Guoping He; Li Dong; Liang Fang; Jinchuan Zhou

Applications of Mathematics (2013)

  • Volume: 58, Issue: 2, page 223-247
  • ISSN: 0862-7940

Abstract

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In this paper we introduce a new smoothing function and show that it is coercive under suitable assumptions. Based on this new function, we propose a smoothing Newton method for solving the second-order cone complementarity problem (SOCCP). The proposed algorithm solves only one linear system of equations and performs only one line search at each iteration. It is shown that any accumulation point of the iteration sequence generated by the proposed algorithm is a solution to the SOCCP. Furthermore, we prove that the generated sequence is bounded if the solution set of the SOCCP is nonempty and bounded. Under the assumption of nonsingularity, we establish the local quadratic convergence of the algorithm without the strict complementarity condition. Numerical results indicate that the proposed algorithm is promising.

How to cite

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Tang, Jingyong, et al. "A smoothing Newton method for the second-order cone complementarity problem." Applications of Mathematics 58.2 (2013): 223-247. <http://eudml.org/doc/252504>.

@article{Tang2013,
abstract = {In this paper we introduce a new smoothing function and show that it is coercive under suitable assumptions. Based on this new function, we propose a smoothing Newton method for solving the second-order cone complementarity problem (SOCCP). The proposed algorithm solves only one linear system of equations and performs only one line search at each iteration. It is shown that any accumulation point of the iteration sequence generated by the proposed algorithm is a solution to the SOCCP. Furthermore, we prove that the generated sequence is bounded if the solution set of the SOCCP is nonempty and bounded. Under the assumption of nonsingularity, we establish the local quadratic convergence of the algorithm without the strict complementarity condition. Numerical results indicate that the proposed algorithm is promising.},
author = {Tang, Jingyong, He, Guoping, Dong, Li, Fang, Liang, Zhou, Jinchuan},
journal = {Applications of Mathematics},
keywords = {second-order cone complementarity problem; smoothing function; smoothing Newton method; global convergence; quadratic convergence; second-order cone complementarity problem; smoothing function; smoothing Newton method; global convergence; quadratic convergence},
language = {eng},
number = {2},
pages = {223-247},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A smoothing Newton method for the second-order cone complementarity problem},
url = {http://eudml.org/doc/252504},
volume = {58},
year = {2013},
}

TY - JOUR
AU - Tang, Jingyong
AU - He, Guoping
AU - Dong, Li
AU - Fang, Liang
AU - Zhou, Jinchuan
TI - A smoothing Newton method for the second-order cone complementarity problem
JO - Applications of Mathematics
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 58
IS - 2
SP - 223
EP - 247
AB - In this paper we introduce a new smoothing function and show that it is coercive under suitable assumptions. Based on this new function, we propose a smoothing Newton method for solving the second-order cone complementarity problem (SOCCP). The proposed algorithm solves only one linear system of equations and performs only one line search at each iteration. It is shown that any accumulation point of the iteration sequence generated by the proposed algorithm is a solution to the SOCCP. Furthermore, we prove that the generated sequence is bounded if the solution set of the SOCCP is nonempty and bounded. Under the assumption of nonsingularity, we establish the local quadratic convergence of the algorithm without the strict complementarity condition. Numerical results indicate that the proposed algorithm is promising.
LA - eng
KW - second-order cone complementarity problem; smoothing function; smoothing Newton method; global convergence; quadratic convergence; second-order cone complementarity problem; smoothing function; smoothing Newton method; global convergence; quadratic convergence
UR - http://eudml.org/doc/252504
ER -

References

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