Michael J. Todd: Semidefinite Programming
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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