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Title: An inexact primal-dual path following algorithm for convex quadratic SDP
Authors: Toh, K.-C. 
Keywords: Inexact search direction
Interior point method
Krylov iterative method
Semidefinite least squares
Semidefinite programming
Issue Date: Mar-2008
Citation: Toh, K.-C. (2008-03). An inexact primal-dual path following algorithm for convex quadratic SDP. Mathematical Programming 112 (1) : 221-254. ScholarBank@NUS Repository.
Abstract: We propose primal-dual path-following Mehrotra-type predictor-corrector methods for solving convex quadratic semidefinite programming (QSDP) problems of the form: equation presented, where Q is a self-adjoint positive semidefinite linear operator on Sn, b R m , and A is a linear map from SSn to R m . At each interior-point iteration, the search direction is computed from a dense symmetric indefinite linear system (called the augmented equation) of dimension m + n(n + 1)/2. Such linear systems are typically very large and can only be solved by iterative methods. We propose three classes of preconditioners for the augmented equation, and show that the corresponding preconditioned matrices have favorable asymptotic eigenvalue distributions for fast convergence under suitable nondegeneracy assumptions. Numerical experiments on a variety of QSDPs with n up to 1600 are performed and the computational results show that our methods are efficient and robust. © 2007 Springer-Verlag.
Source Title: Mathematical Programming
ISSN: 00255610
DOI: 10.1007/s10107-006-0088-y
Appears in Collections:Staff Publications

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