plenary talk at the One-day Optimization Workshop, at McMaster University, Aug. 4, 2000, in the JHE building, room A114.

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

This talk is partly based on several papers; principally, on the papers dealing with 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. A new summary with new results on the EDM completion problem is in the CORR report Semidefinite Programming for Discrete Optimization and Matrix Completion Problems, June, 2000