Please use this identifier to cite or link to this item: https://scholarbank.nus.edu.sg/handle/10635/102728
Title: A polynomial-time inexact primal-dual infeasible path-following algorithm for convex quadratic SDP
Authors: Li, L.
Toh, K.-C. 
Keywords: Inexact search direction
Infeasible interior point method
Polynomial complexity
Semidefinite least squares
Semidefinite programming
Issue Date: Jan-2011
Citation: Li, L.,Toh, K.-C. (2011-01). A polynomial-time inexact primal-dual infeasible path-following algorithm for convex quadratic SDP. Pacific Journal of Optimization 7 (1) : 43-61. ScholarBank@NUS Repository.
Abstract: Convex quadratic semidefinite programming (QSDP) has been widely applied in solving engineering and scientific problems such as nearest correlation problems and nearest Euclidean distance matrix problems. In this paper, we study an inexact primal-dual infeasible path-following algorithm for QSDP problems of the form: minX{1/2 X • Q(X) + C • X: A(X) = b, X ≥ 0}, where Q is a self-adjoint positive semidefinite linear operator on Sn, b ∈ Rm, and A is a linear map from Sn to Rm. This algorithm is designed for the purpose of using an iterative solver to compute an approximate search direction at each iteration. It does not require feasibility to be maintained even if some iterates happened to be feasible. By imposing mild conditions on the inexactness of the computed directions, we show that the algorithm can find an ∈-solution in O(n2 ln(1/∈)) iterations. © Yokohama Publishers.
Source Title: Pacific Journal of Optimization
URI: http://scholarbank.nus.edu.sg/handle/10635/102728
ISSN: 13489151
Appears in Collections:Staff Publications

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