TY - JOUR
T1 - The Jacobian consistency of a smoothed Fischer-Burmeister function associated with second-order cones
AU - Ogasawara, Hideho
AU - Narushima, Yasushi
N1 - Funding Information:
The authors would like to express their appreciation to Prof. Nobuko Sagara of the Institute of Managerial Research, Aichi University for her valuable comments that helped in accomplishing this paper. The authors are supported in part by the Grant-in-Aid for Scientific Research (C) 21510164 of Japan Society for the Promotion of Science .
PY - 2012/10/1
Y1 - 2012/10/1
N2 - This paper deals with the second-order cone complementarity problem (SOCCP), which is an important class of problems containing various optimization problems. The SOCCP can be reformulated as a system of nonsmooth equations. For solving this system of nonsmooth equations, smoothing Newton methods are widely used. The Jacobian consistency property plays an important role for achieving a rapid convergence of the methods. In this paper, we show the Jacobian consistency of a smoothed Fischer-Burmeister function. Moreover, we estimate the distance between the subgradient of the Fischer-Burmeister function and the gradient of its smoothing function.
AB - This paper deals with the second-order cone complementarity problem (SOCCP), which is an important class of problems containing various optimization problems. The SOCCP can be reformulated as a system of nonsmooth equations. For solving this system of nonsmooth equations, smoothing Newton methods are widely used. The Jacobian consistency property plays an important role for achieving a rapid convergence of the methods. In this paper, we show the Jacobian consistency of a smoothed Fischer-Burmeister function. Moreover, we estimate the distance between the subgradient of the Fischer-Burmeister function and the gradient of its smoothing function.
KW - Jacobian consistency
KW - Second-order cone complementarity problem
KW - Smoothed Fischer-Burmeister function
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U2 - 10.1016/j.jmaa.2012.04.050
DO - 10.1016/j.jmaa.2012.04.050
M3 - Article
AN - SCOPUS:84861661061
SN - 0022-247X
VL - 394
SP - 231
EP - 247
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
ER -