Abstract
We introduce an entropy-like proximal algorithm for the problem of minimizing a closed proper convex function subject to symmetric cone constraints. The algorithm is based on a distance-like function that is an extension of the Kullback- Leiber relative entropy to the setting of symmetric cones. Like the proximal algorithms for convex programming with nonnegative orthant cone constraints, we show that, under some mild assumptions, the sequence generated by the proposed algorithm is bounded and every accumulation point is a solution of the considered problem. In addition, we also present a dual application of the proposed algorithm to the symmetric cone linear program, leading to a multiplier method which is shown to possess similar properties as the exponential multiplier method (Tseng and Bertsekas in Math. Program. 60:1-19, 1993) holds.
| Original language | English |
|---|---|
| Pages (from-to) | 477-499 |
| Number of pages | 23 |
| Journal | Computational Optimization and Applications |
| Volume | 47 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2010 Nov 1 |
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Keywords
- Entropy-like distance
- Exponential multiplier method
- Proximal-like method
- Symmetric cone optimization
ASJC Scopus subject areas
- Control and Optimization
- Computational Mathematics
- Applied Mathematics
Cite this
An entropy-like proximal algorithm and the exponential multiplier method for convex symmetric cone programming. / Chen, Jein-Shan; Pan, Shaohua.
In: Computational Optimization and Applications, Vol. 47, No. 3, 01.11.2010, p. 477-499.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - An entropy-like proximal algorithm and the exponential multiplier method for convex symmetric cone programming
AU - Chen, Jein-Shan
AU - Pan, Shaohua
PY - 2010/11/1
Y1 - 2010/11/1
N2 - We introduce an entropy-like proximal algorithm for the problem of minimizing a closed proper convex function subject to symmetric cone constraints. The algorithm is based on a distance-like function that is an extension of the Kullback- Leiber relative entropy to the setting of symmetric cones. Like the proximal algorithms for convex programming with nonnegative orthant cone constraints, we show that, under some mild assumptions, the sequence generated by the proposed algorithm is bounded and every accumulation point is a solution of the considered problem. In addition, we also present a dual application of the proposed algorithm to the symmetric cone linear program, leading to a multiplier method which is shown to possess similar properties as the exponential multiplier method (Tseng and Bertsekas in Math. Program. 60:1-19, 1993) holds.
AB - We introduce an entropy-like proximal algorithm for the problem of minimizing a closed proper convex function subject to symmetric cone constraints. The algorithm is based on a distance-like function that is an extension of the Kullback- Leiber relative entropy to the setting of symmetric cones. Like the proximal algorithms for convex programming with nonnegative orthant cone constraints, we show that, under some mild assumptions, the sequence generated by the proposed algorithm is bounded and every accumulation point is a solution of the considered problem. In addition, we also present a dual application of the proposed algorithm to the symmetric cone linear program, leading to a multiplier method which is shown to possess similar properties as the exponential multiplier method (Tseng and Bertsekas in Math. Program. 60:1-19, 1993) holds.
KW - Entropy-like distance
KW - Exponential multiplier method
KW - Proximal-like method
KW - Symmetric cone optimization
UR - http://www.scopus.com/inward/record.url?scp=78650067900&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=78650067900&partnerID=8YFLogxK
U2 - 10.1007/s10589-008-9227-0
DO - 10.1007/s10589-008-9227-0
M3 - Article
AN - SCOPUS:78650067900
VL - 47
SP - 477
EP - 499
JO - Computational Optimization and Applications
JF - Computational Optimization and Applications
SN - 0926-6003
IS - 3
ER -