NDLI: Some New Search Directions for Primal-Dual Interior Point Methods in Semidefinite Programming

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Toh, Kim-Chuan
Copyright Year	2000
Abstract	Search directions for primal-dual path-following methods for semidefinite programming (SDP) are proposed. These directions have the properties that (1) under certain nondegeneracy and strict complementarity assumptions, the Jacobian matrix of the associated symmetrized Newton equation has a bounded condition number along the central path in the limit as the barrier parameter $\mu$ tends to zero; and (2) the Schur complement matrix of the symmetrized Newton equation is symmetric and the cost for computing this matrix is 2mn3 + 0.5m2n2 flops, where n and m are the dimension of the matrix and vector variables of the semidefinite program, respectively. These two properties imply that a path-following method using the proposed directions can achieve the high accuracy typically attained by methods employing the direction proposed by Alizadeh, Haeberly, and Overton (currently the best search direction in terms of accuracy), but each iteration requires at most half the amount of flops (to leading order).
Starting Page	223
Ending Page	242
Page Count	20
File Format	PDF
ISSN	10526234
DOI	10.1137/S1052623498335067
e-ISSN	10957189
Journal	SIAM Journal on Optimization (SJOPE8)
Issue Number	1
Volume Number	11
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-31
Access Restriction	Subscribed
Subject Keyword	semidefinite programming interior point methods Linear programming search directions
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Theoretical Computer Science Software

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