## Semidefinite Programming Problems

Semidefinite programming involves the minimization of a linear function
subject to the constraint that an affine combination of symmetric matrices
is positive semidefinite. This constraint is in general nonlinear
and nonsmooth yet convex. Semidefinite programming can be viewed as an extension of
linear programming and reduces to the linear programming case when the symmetric
matrices are diagonal. The two main areas of application for semidefinite programming
are in combinatorial optimization and control theory.

### Test Collections

A set of max-cut test problems is available at
ftp://dollar.biz.uiowa.edu/pub/yyye/Gset.
Toh, et.al.(1998), provide matlab files to generate random instances of
semidefinite programming applications. These files, available at
http://www.math.cmu.edu/~reha/sdpt3.html
generate instances of the following problem types:

- maximum eigenvalue determination
- matrix norm minimization
- Chebychev approximation problem for a matrix
- logarithmic Chebychev approximation
- Chebychev approximation on the complex plane
- control and system problem
- relaxation of the max-cut problem
- relaxation of the stable set problem
- the educational testing problem

A library of semidefinite programming test problems SDPLIB can be found at
http://www.nmt.edu/~borchers/sdplib.html.

Second order cone programming test problems may be found at
http://dragon.princeton.edu:80/~rvdb/ampl/nlmodels/sdp/.

### Test Problem

Test Problem |
Description |
Gams File |

1 |
The Educational Testing Problem |
.gms |

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