Semidefinite programming (SDP) is concerned with optimizing a linear function of a symmetric matrix, subject to linear constraints and the requirement that the matrix be positive semidefinite. This problem finds diverse applications in systems and control theory, in eigenvalue optimization, in tight relaxations of NP-hard combinatorial optimization problems, in statistics, and in quasi-Newton updates in nonlinear optimization. For more details, see the SDP home pages below. I have been interested in developing and analyzing primal-dual interior-point methods for solving such problems and slight generalizations thereof (self-scaled conic problems) with Yurii Nesterov. I have also been interested in analyzing and comparing these and other methods, and in developing efficient implementations, jointly with Kim Chuan Toh and Reha Tütüncü. We have a MATLAB software package, SDPT3, which can handle conic programming problems involving any combination of semidefinite, second-order, and nonnegative cone constraints, available here. Some benchmarks comparing SDPT3 to other software on a variety of test problem suites can be found at Hans Mittelmann's site. My papers on SDP and other topics are here.
The Interior Point Methods On-Line Site, run by
Steve Wright.
Two semidefinite programming sites: the
first by
Farid Alizadeh and the
second
by
Christoph Helmberg;
see also the
papers
on eigenvalue optimization and
semidefinite programming by
Michael Overton.
The output of Jon Kleinberg's program on "+semidefinite+programming"
(in January 1999) is here.