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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:

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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