TY - JOUR
T1 - A regularization method for the second-order cone complementarity problem with the Cartesian P0-property
AU - Pan, Shaohua
AU - Chen, Jein Shan
N1 - Funding Information:
The authors would like to thank Prof. Paul Tseng for his helpful suggestions on improving the presentation of this paper. The second author’s work is partially supported by the National Science Council of Taiwan.
PY - 2009/2/15
Y1 - 2009/2/15
N2 - We consider the Tikhonov regularization method for the second-order cone complementarity problem (SOCCP) with the Cartesian P0-property. We show that many results of the regularization method for the P0-nonlinear complementarity problem still hold for this important class of nonmonotone SOCCP. For example, under the more general setting, every regularized problem has the unique solution, and the solution trajectory generated is bounded if the original SOCCP has a nonempty and bounded solution set. We also propose an inexact regularization algorithm by solving the sequence of regularized problems approximately with the merit function approach based on Fischer-Burmeister merit function, and establish the convergence result of the algorithm. Preliminary numerical results are also reported, which verify the favorable theoretical properties of the proposed method.
AB - We consider the Tikhonov regularization method for the second-order cone complementarity problem (SOCCP) with the Cartesian P0-property. We show that many results of the regularization method for the P0-nonlinear complementarity problem still hold for this important class of nonmonotone SOCCP. For example, under the more general setting, every regularized problem has the unique solution, and the solution trajectory generated is bounded if the original SOCCP has a nonempty and bounded solution set. We also propose an inexact regularization algorithm by solving the sequence of regularized problems approximately with the merit function approach based on Fischer-Burmeister merit function, and establish the convergence result of the algorithm. Preliminary numerical results are also reported, which verify the favorable theoretical properties of the proposed method.
KW - Cartesian P-property
KW - Fischer-Burmeister merit function
KW - Second-order cone complementarity problem
KW - Tikhonov regularization
UR - http://www.scopus.com/inward/record.url?scp=57049142204&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=57049142204&partnerID=8YFLogxK
U2 - 10.1016/j.na.2008.02.028
DO - 10.1016/j.na.2008.02.028
M3 - Article
AN - SCOPUS:57049142204
SN - 0362-546X
VL - 70
SP - 1475
EP - 1491
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
IS - 4
ER -