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 in the restricted SDP setting, and in developing efficient implementations, jointly with Kim Chuan Toh and Reha Tütüncü. We have a MATLAB software package, SDPT3, available here. 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" is here.

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