## SDPT3 version 4.0 -- a MATLAB software for semidefinite-quadratic-linear programming

### Kim-Chuan Toh, Michael J. Todd, Reha H. Tutuncu

The last major update on the software was in Feb 2009. It implemented an infeasible path-following algorithm (sqlp.m) for solving SQLP -- conic optimization problems involving semidefinite, second-order and linear cone constraints. It also has a path-following algorithm (HSDsqlp.m) for solving a 3-parameter homogeneous self-dual reformulation of SQLP. Note: though this software is fairly well tested, but minor refinement or fix may still be needed from time to time.

New features that SDPT3 can now handle:

• free variables;
• determinant maximization problems;
• SDP with complex data;
• 3-parameter homogeneous self-dual model of SQLP (in HSDsqlp.m);

#### Citation

• K.C. Toh, M.J. Todd, and R.H. Tutuncu, SDPT3 --- a Matlab software package for semidefinite programming, Optimization Methods and Software, 11 (1999), pp. 545--581.
• R.H Tutuncu, K.C. Toh, and M.J. Todd, Solving semidefinite-quadratic-linear programs using SDPT3, Mathematical Programming Ser. B, 95 (2003), pp. 189--217.

• SDPT3 is currently used as one of the main computational engines in optimization modeling languages such as CVX and YALMIP .

• Please read.. Welcome to SDPT3-4.0! The software is built for MATLAB version 7.4 or later releases, it may not work for earlier versions. The software requires a few Mex files for execution. You can generate the Mex files as follows:

• Run Matlab in the directory SDPT3-4.0

• In Matlab command window, type:

xxxxxxxxxx>>installmex(1)
• After that, to see whether you have installed SDPT3 correctly, type:

xxxxxxxxxx>> startup>> sqlpdemo
• By now, SDPT3 is ready for you to use.

• User's guide (PDF)

• The following example shows how SDPT3 call a data file that is stored in SDPA format:

xxxxxxxxxx>> [blk,At,C,b] = read_sdpa('/sdplib/theta3.dat-s'); >> [obj,X,y,Z] = sdpt3(blk,At,C,b);

The following example shows how SDPT3 call a data file that is stored in SeDuMi format:

xxxxxxxxxx>> [blk,At,C,b] = read_sedumi(AA,bb,cc,K); or [blk,At,C,b] = read_sedumi('/dimacs/hamming_7_5_6.mat');>> [obj,X,y,Z] = sdpt3(blk,At,C,b);
• Simple examples to illustrate the usage of the software

• Special thanks go to Hans Mittelmann for his effort in benchmarking several SDP software packages on the following test problems:

benchmark on some large sparse SDPs;

benchmark on SDPs with free variables;

### Bugs corrected

• 2017/08/23: fixed a bug (reported by Johan Lofberg) due to mex-function incompatibility with MatlabR2016
• 2017/05/06: fixed a bug reported by Johan Lofberg
• 2017/05/06: fixed mex-function incompatibility with MatlabR2016a
• 2016/10/26: fixed mex-function incompatibility with MatlabR2015b

### Acknowledgements

We thank those who had made suggestions and reported bugs to make SDPT3 better. In particular, we thank Johan Lofberg for bug reports while incorporating SDPT3 into YALMIP. Thanks also go to Michael Grant for bug reports while testing SDPT3 as an engine for CVX.