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Symmetric primal-dual path-following algorithms for semidefinite programming

✍ Scribed by Jos F. Sturm; Shuzhong Zhang

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
667 KB
Volume
29
Category
Article
ISSN
0168-9274

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✦ Synopsis

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.

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