ISSN:
1573-2894
Keywords:
positive definite completions
;
best nonnegative approximation
;
semidefinite programming
;
primal-dual interior-point methods
;
complementarity problems
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
Notes:
Abstract Given a nonnegative, symmetric matrix of weights, H, we study the problem of finding an Hermitian, positive semidefinite matrix which is closest to a given Hermitian matrix, A, with respect to the weighting H. This extends the notion of exact matrix completion problems in that, H ij =0 corresponds to the element A ij being unspecified (free), while H ij large in absolute value corresponds to the element A ij being approximately specified (fixed). We present optimality conditions, duality theory, and two primal-dual interior-point algorithms. Because of sparsity considerations, the dual-step-first algorithm is more efficient for a large number of free elements, while the primal-step-first algorithm is more efficient for a large number of fixed elements. Included are numerical tests that illustrate the efficiency and robustness of the algorithms
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1018363021404
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