First- and second-order methods for semidefinite programming

First- and second-order methods for semidefinite programming

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Article ID: iaor20041767
Country: Germany
Volume: 97
Issue: 1/2
Start Page Number: 209
End Page Number: 244
Publication Date: Jan 2003
Journal: Mathematical Programming
Authors:
Keywords: semidefinite programming
Abstract:

In this paper, we survey the most recent methods that have been developed for the solution of semi-definite programs. We first concentrate on the methods that have been primarily motivated by the interior point (IP) algorithms for linear programming, putting special emphasis in the class of primal–dual path-following algorithms. We also survey methods that have been developed for solving large-scale SDP problems. These include first-order nonlinear programming methods and more specialized path-following IP methods which use the (preconditioned) conjugate gradient or residual scheme to compute the Newton direction and the notion of matrix completion to exploit data sparsity.

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