Abstract
In this article, we show that a one-parametric class of SOC merit functions has a Lipschitz continuous gradient; and moreover, the Lipschitz constant is related to the parameter in this class of SOC merit functions. This fact will lay a building block when the merit function approach as well as the Newton-type method are employed for solving the second-order cone complementarity problem with this class of merit functions.
| Original language | English |
|---|---|
| Pages (from-to) | 661-676 |
| Number of pages | 16 |
| Journal | Optimization |
| Volume | 59 |
| Issue number | 5 |
| DOIs | |
| Publication status | Published - 2010 Jul 1 |
Fingerprint
Keywords
- Lipschitz continuity
- Merit function
- Second-order cone
- Spectral factorization
ASJC Scopus subject areas
- Control and Optimization
- Management Science and Operations Research
- Applied Mathematics
Cite this
Lipschitz continuity of the gradient of a one-parametric class of SOC merit functions. / Chen, Jein Shan; Pan, Shaohua.
In: Optimization, Vol. 59, No. 5, 01.07.2010, p. 661-676.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Lipschitz continuity of the gradient of a one-parametric class of SOC merit functions
AU - Chen, Jein Shan
AU - Pan, Shaohua
PY - 2010/7/1
Y1 - 2010/7/1
N2 - In this article, we show that a one-parametric class of SOC merit functions has a Lipschitz continuous gradient; and moreover, the Lipschitz constant is related to the parameter in this class of SOC merit functions. This fact will lay a building block when the merit function approach as well as the Newton-type method are employed for solving the second-order cone complementarity problem with this class of merit functions.
AB - In this article, we show that a one-parametric class of SOC merit functions has a Lipschitz continuous gradient; and moreover, the Lipschitz constant is related to the parameter in this class of SOC merit functions. This fact will lay a building block when the merit function approach as well as the Newton-type method are employed for solving the second-order cone complementarity problem with this class of merit functions.
KW - Lipschitz continuity
KW - Merit function
KW - Second-order cone
KW - Spectral factorization
UR - http://www.scopus.com/inward/record.url?scp=77953841171&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=77953841171&partnerID=8YFLogxK
U2 - 10.1080/02331930802180319
DO - 10.1080/02331930802180319
M3 - Article
AN - SCOPUS:77953841171
VL - 59
SP - 661
EP - 676
JO - Optimization
JF - Optimization
SN - 0233-1934
IS - 5
ER -