TY - JOUR
T1 - Symmetric primal-dual path-following algorithms for semidefinite programming
AU - Sturm, Jos F.
AU - Zhang, Shuzhong
PY - 1999/3
Y1 - 1999/3
N2 - We propose a framework for developing and analyzing primal-dual interior point algorithms for semidefinite programming. This framework is an extension of the v-space approach that was developed by Kojima et al. (1991) for linear complementarity problems. The extension to semidefinite programming allows us to interpret Nesterov-Todd type directions (Nesterov and Todd 1995, 1997) as Newton search directions. Our approach does not involve any barrier function. Several primal-dual path-following algorithms for semidefinite programming are analyzed. The treatment of these algorithms for semidefinite programming in our setting bears great similarity to the linear programming case.
AB - We propose a framework for developing and analyzing primal-dual interior point algorithms for semidefinite programming. This framework is an extension of the v-space approach that was developed by Kojima et al. (1991) for linear complementarity problems. The extension to semidefinite programming allows us to interpret Nesterov-Todd type directions (Nesterov and Todd 1995, 1997) as Newton search directions. Our approach does not involve any barrier function. Several primal-dual path-following algorithms for semidefinite programming are analyzed. The treatment of these algorithms for semidefinite programming in our setting bears great similarity to the linear programming case.
KW - Primal-dual interior point method
KW - Primal-dual transformation
KW - Semidefinite programming
UR - http://www.scopus.com/inward/record.url?scp=0000768180&partnerID=8YFLogxK
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U2 - 10.1016/S0168-9274(98)00099-3
DO - 10.1016/S0168-9274(98)00099-3
M3 - Article
AN - SCOPUS:0000768180
SN - 0168-9274
VL - 29
SP - 301
EP - 315
JO - Applied Numerical Mathematics
JF - Applied Numerical Mathematics
IS - 3
ER -