TY - JOUR
T1 - Polynomial primal-dual cone affine scaling for semidefinite programming
AU - Berkelaar, Arjan B.
AU - Sturm, Jos F.
AU - Zhang, Shuzhong
PY - 1999/3
Y1 - 1999/3
N2 - Semidefinite programming concerns the problem of optimizing a linear function over a section of the cone of semidefinite matrices. In the cone affine scaling approach, we replace the cone of semidefinite matrices by a certain inscribed cone, in such a way that the resulting optimization problem is analytically solvable. The now easily obtained solution to this modified problem serves as an approximate solution to the semidefinite programming problem. The inscribed cones that we use are affine transformations of second order cones, hence the name 'cone affine scaling'. Compared to other primal-dual affine scaling algorithms for semidefinite programming (see de Klerk, Roos and Terlaky (1997)), our algorithm enjoys the lowest computational complexity.
AB - Semidefinite programming concerns the problem of optimizing a linear function over a section of the cone of semidefinite matrices. In the cone affine scaling approach, we replace the cone of semidefinite matrices by a certain inscribed cone, in such a way that the resulting optimization problem is analytically solvable. The now easily obtained solution to this modified problem serves as an approximate solution to the semidefinite programming problem. The inscribed cones that we use are affine transformations of second order cones, hence the name 'cone affine scaling'. Compared to other primal-dual affine scaling algorithms for semidefinite programming (see de Klerk, Roos and Terlaky (1997)), our algorithm enjoys the lowest computational complexity.
KW - Affine scaling
KW - Primal-dual interior point methods
KW - Semidefinite programming
UR - http://www.scopus.com/inward/record.url?scp=0040437615&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0040437615&partnerID=8YFLogxK
U2 - 10.1016/S0168-9274(98)00100-7
DO - 10.1016/S0168-9274(98)00100-7
M3 - Article
AN - SCOPUS:0040437615
SN - 0168-9274
VL - 29
SP - 317
EP - 333
JO - Applied Numerical Mathematics
JF - Applied Numerical Mathematics
IS - 3
ER -