On extending some primal-dual interior-point algorithms from linear programming to semidefinite programming (1998) [39 citations — 1 self]
|
Popular Tags
No tags have been applied to this document.
BibTeX | Add To MetaCart
@ARTICLE{Zhang98onextending,author = {Yin Zhang},
title = {On extending some primal-dual interior-point algorithms from linear programming to semidefinite programming},
journal = {SIAM Journal on Optimization},
year = {1998},
volume = {8},
pages = {365--386}
}
Years of Citing Articles
Abstract:
This work concerns primal-dual interior-point methods for semidefinite programming (SDP) that use a search direction originally proposed by Helmberg-Rendl-Vanderbei-Wolkowicz [5] and Kojima-Shindoh-Hara [11], and recently rediscovered by Monteiro [15] in a more explicit form. In analyzing these methods, a number of basic equalities and inequalities were developed in [11] and also in [15] through different means and in different forms. In this paper, we give a concise derivation of the key equalities and inequalities for complexity analysis along the exact line used in linear programming (LP), producing basic relationships that have compact forms almost identical to their counterparts in LP. We also introduce a new formulation of the central path and variable-metric measures of centrality. These results provide convenient tools for deriving polynomiality results for primal-dual algorithms extended from LP to SDP using the aforementioned and related search directions. We present examples of such extensions, including the long-step infeasible-interior-point algorithm of Zhang [25]. Keywords: Semidefinite programming, Primal-Dual interior-point methods.
