presentation at the meeting on Optimization and Applications at Mathematisches Forschungsinstitut Oberwolfach, Jan 13-19/02.

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

This talk is based on several papers; principally, on the papers dealing with semidefinite programming and its applications. The book
HANDBOOK OF SEMIDEFINITE PROGRAMMING: Theory, Algorithms, and Applications, Kluwer, Feb. 2000, provides the main source of the material.
Details results appear in the papers: Simple Efficient Solutions for Semidefinite Programming and A Simple Iterative Method for Linear Programming

colloquium talk at Lehrstuhl für Mathematische Optimierung, Duesseldorf, Friday, Jan. 11, 2002, 5PM.

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

This talk is 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 three papers:
AN INTERIOR-POINT METHOD FOR APPROXIMATE POSITIVE SEMIDEFINITE COMPLETIONS and
Solving Euclidean distance matrix completion problems via semidefinite programming and Two Theorems On Euclidean Distance Matrices and Gale Transform
present primal-dual interior-point methods/theory 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.