Abstract
We investigate some properties related to the generalized Newton method for the Fischer-Burmeister (FB) function over second-order cones, which allows us to reformulate the second-order cone complementarity problem (SOCCP) as a semismooth system of equations. Specifically, we characterize the B-subdifferential of the FB function at a general point and study the condition for every element of the B-subdifferential at a solution being nonsingular. In addition, for the induced FB merit function, we establish its coerciveness and provide a weaker condition than Chen and Tseng (Math. Program. 104:293-327, 2005) for each stationary point to be a solution, under suitable Cartesian P-properties of the involved mapping. By this, a damped Gauss-Newton method is proposed, and the global and superlinear convergence results are obtained. Numerical results are reported for the second-order cone programs from the DIMACS library, which verify the good theoretical properties of the method.
| Original language | English |
|---|---|
| Pages (from-to) | 293-318 |
| Number of pages | 26 |
| Journal | Applied Mathematics and Optimization |
| Volume | 59 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2009 Jun 1 |
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Keywords
- B-subdifferential
- Complementarity
- Fischer-Burmeister function
- Generalized Newton method
- Second-order cones
ASJC Scopus subject areas
- Applied Mathematics
- Control and Optimization
Cite this
A damped Gauss-Newton method for the second-order cone complementarity problem. / Pan, Shaohua; Chen, Jein-Shan.
In: Applied Mathematics and Optimization, Vol. 59, No. 3, 01.06.2009, p. 293-318.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A damped Gauss-Newton method for the second-order cone complementarity problem
AU - Pan, Shaohua
AU - Chen, Jein-Shan
PY - 2009/6/1
Y1 - 2009/6/1
N2 - We investigate some properties related to the generalized Newton method for the Fischer-Burmeister (FB) function over second-order cones, which allows us to reformulate the second-order cone complementarity problem (SOCCP) as a semismooth system of equations. Specifically, we characterize the B-subdifferential of the FB function at a general point and study the condition for every element of the B-subdifferential at a solution being nonsingular. In addition, for the induced FB merit function, we establish its coerciveness and provide a weaker condition than Chen and Tseng (Math. Program. 104:293-327, 2005) for each stationary point to be a solution, under suitable Cartesian P-properties of the involved mapping. By this, a damped Gauss-Newton method is proposed, and the global and superlinear convergence results are obtained. Numerical results are reported for the second-order cone programs from the DIMACS library, which verify the good theoretical properties of the method.
AB - We investigate some properties related to the generalized Newton method for the Fischer-Burmeister (FB) function over second-order cones, which allows us to reformulate the second-order cone complementarity problem (SOCCP) as a semismooth system of equations. Specifically, we characterize the B-subdifferential of the FB function at a general point and study the condition for every element of the B-subdifferential at a solution being nonsingular. In addition, for the induced FB merit function, we establish its coerciveness and provide a weaker condition than Chen and Tseng (Math. Program. 104:293-327, 2005) for each stationary point to be a solution, under suitable Cartesian P-properties of the involved mapping. By this, a damped Gauss-Newton method is proposed, and the global and superlinear convergence results are obtained. Numerical results are reported for the second-order cone programs from the DIMACS library, which verify the good theoretical properties of the method.
KW - B-subdifferential
KW - Complementarity
KW - Fischer-Burmeister function
KW - Generalized Newton method
KW - Second-order cones
UR - http://www.scopus.com/inward/record.url?scp=63049104088&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=63049104088&partnerID=8YFLogxK
U2 - 10.1007/s00245-008-9054-9
DO - 10.1007/s00245-008-9054-9
M3 - Article
VL - 59
SP - 293
EP - 318
JO - Applied Mathematics and Optimization
JF - Applied Mathematics and Optimization
SN - 0095-4616
IS - 3
ER -