TY - JOUR
T1 - A Smoothing Newton Method with Fischer-Burmeister Function for Second-Order Cone Complementarity Problems
AU - Narushima, Yasushi
AU - Sagara, Nobuko
AU - Ogasawara, Hideho
N1 - Funding Information:
The authors would like to express our appreciation to the associate editor and the referee for valuable comments and suggestions, which have greatly improved the exposition. The first and third authors are supported in part by the Grant-in-Aid for Scientific Research (C) 21510164 of Japan Society for the Promotion of Science.
PY - 2011/2
Y1 - 2011/2
N2 - The second-order cone complementarity problem (SOCCP) is an important class of problems containing a lot of optimization problems. The SOCCP can be transformed into a system of nonsmooth equations. To solve this nonsmooth system, smoothing techniques are often used. Fukushima, Luo and Tseng (SIAM J. Optim. 12:436-460, 2001) studied concrete theories and properties of smoothing functions for the SOCCP. Recently, a practical computational method using the smoothed natural residual function to solve the SOCCP was given by Chen, Sun and Sun (Comput. Optim. Appl. 25:39-56, 2003). In the present paper, we propose an algorithm to solve the SOCCP by using the smoothed Fischer-Burmeister function. Some preliminary numerical results are given.
AB - The second-order cone complementarity problem (SOCCP) is an important class of problems containing a lot of optimization problems. The SOCCP can be transformed into a system of nonsmooth equations. To solve this nonsmooth system, smoothing techniques are often used. Fukushima, Luo and Tseng (SIAM J. Optim. 12:436-460, 2001) studied concrete theories and properties of smoothing functions for the SOCCP. Recently, a practical computational method using the smoothed natural residual function to solve the SOCCP was given by Chen, Sun and Sun (Comput. Optim. Appl. 25:39-56, 2003). In the present paper, we propose an algorithm to solve the SOCCP by using the smoothed Fischer-Burmeister function. Some preliminary numerical results are given.
KW - Fischer-Burmeister function
KW - Global convergence
KW - Second-order cone complementarity problem
KW - Smoothing method
KW - Superlinear convergence
UR - http://www.scopus.com/inward/record.url?scp=79952105634&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=79952105634&partnerID=8YFLogxK
U2 - 10.1007/s10957-010-9776-0
DO - 10.1007/s10957-010-9776-0
M3 - Article
AN - SCOPUS:79952105634
SN - 0022-3239
VL - 149
SP - 79
EP - 101
JO - Journal of Optimization Theory and Applications
JF - Journal of Optimization Theory and Applications
IS - 1
ER -