Semidefinite Programming and Matrix Completion

talk at Seventh SIAM Conference on Applied Linear Algebra, Oct. 23-26, 2000.

(The
Abstract (text file):;
the
presentation (ps file))

An expanded version of this talk will be given in the
dept of O.R. at the
University of North Carolina , Chapel Hill, on Thursday Oct 26.

This talk is based on several papers; principally, on the papers
dealing with completion problems.
The paper (in progress)

New Semidefinite Programming Model for Large Sparse
Euclidean Distance Matrix Completion Problems.

The paper

Positive definite completions of partial {H}ermitian matrices
(GRONE, B. and JOHNSON, C.R. and MARQUES de SA, E. and WOLKOWICZ, H.)
presents a characterization for completion using chordality of graphs;

while the two papers:

AN INTERIOR-POINT METHOD FOR APPROXIMATE POSITIVE
SEMIDEFINITE COMPLETIONS and

Solving Euclidean distance matrix completion problems via
semidefinite programming

present primal-dual interior-point methods for solving approximate
completion problems. A summary of these results is presented in

Matrix Completion Problems, in the
Handbook of Semidefinite Programming, Kluwer Academic, 2000.