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Inexact primal-dual path-following algorithms for a special class of convex quadratic SDP and related problems

K. C. Toh (mattohkc***at***nus.edu.sg)
R. H. Tutuncu (reha***at***cmu.edu)
M. J. Todd (miketodd***at***cs.cornell.edu)

Abstract: We propose a primal-dual path-following Mehrotra-type predictor-corrector method for solving convex quadratic semidefinite programming (QSDP) problems. For the special case when the quadratic term has the form $\frac{1}{2} X \bul (UXU)$, we compute the search direction at each iteration from the Schur complement equation. We are able to solve the Schur complement equation efficiently via the preconditioned symmetric quasi-minimal residual iterative solver with two appropriately constructed preconditioners. Numerical experiments on a variety of QSDPs with matrices of dimensions up to 2000 are performed and the computational results show that our methods are efficient and robust. Our methods can also be extended to linear SDP problems with upper bound constraints on primal matrix variables.

Keywords: semidefinite programming, semidefinite least squares, path-following methods, Nesterov-Todd scaling, symmetric quasi-minimum residual iteration

Category 1: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Citation: Technical Report 1421, School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY 14853, February 2005.

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Entry Submitted: 03/11/2005
Entry Accepted: 03/11/2005
Entry Last Modified: 12/28/2005

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