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Conic solvers

In this section we provide some notes about our usage experience with VSDP and the following approximate conic solvers.

For our tests we tried the following four combinations to run the conic solver:

+---------------------------+
|      <conic solver>       |
+---------------------------+
|       VSDP & INTLAB       |
+------------+--------------+
|   MATLAB   |  GNU Octave  |
+------------+--------------+

CSDP

• Website: https://github.com/coin-or/Csdp

• Documentation: https://github.com/coin-or/Csdp/blob/master/doc/csdpuser.pdf

• Cones: (Free variables), LP, SDP

• Installation: Binary distributions for Windows and Linux on the website. Extract binary distribution to arbitrary location and use addpath within Octave or MATLAB to add the bin (solver executables) and matlab (interface routines) subdirectories.

• Invocation: Call csdp from the Octave or MATLAB command prompt.

• Notes: Free variables are only supported as difference of LP variables. The resulting problem is ill-posed.

GLPK

• Website: https://www.gnu.org/software/glpk

• Documentation: Part of the source code archive available from the website.

• Cones: Free variables, LP

• Installation: Built-in solver of GNU Octave.

• Invocation: Call glpk from the Octave command prompt.

• Notes: Not available for MATLAB.

LINPROG

• Website: https://www.mathworks.com/help/optim/ug/linprog.html

• Documentation: See website.

• Cones: Free variables, LP

• Installation: Built-in solver of MATLAB.

• Invocation: Call linprog from the MATLAB command prompt.

• Notes: Not available for GNU Octave.

lp_solve

• Website: http://lpsolve.sourceforge.net/5.5/index.htm

• Documentation: See website.

• Cones: Free variables, LP

• Installation: Binary distributions for Windows and Linux are available from https://sourceforge.net/projects/lpsolve/files/lpsolve/5.5.2.5. For Linux it is easier to install the binary solver files from the respective distribution package manager. The Octave and MATLAB interface is available from https://github.com/vsdp/lp_solve or https://sourceforge.net/projects/lpsolve/files/lpsolve/5.5.2.5. Inside the extra/octave/lpsolve or extra/matlab/lpsolve subdirectory one has to follow the build instructions and has to use addpath within Octave or MATLAB to make it work.

• Invocation: Call lp_solve from the Octave or MATLAB command prompt.

MOSEK

• Website: https://www.mosek.com/

• Documentation: https://www.mosek.com/documentation/

• Cones: Free variables, LP, SOCP, SDP

• Installation: Binary distributions for Windows and Linux on the website. Very good description is given at https://docs.mosek.com/8.1/install/installation.html

• Invocation: Call mosekopt from the Octave or MATLAB command prompt.

• Notes: One has to obtain a license, which is gratis for personal and academic use. No Octave. There is some no longer maintained octmosek Octave package, that does notes work for recent Octave versions.

SDPA

• Website: http://sdpa.sourceforge.net

• GitHub: https://github.com/vsdp/sdpa

• Documentation: https://sourceforge.net/projects/sdpa/files/sdpa/sdpa.7.1.1.manual.20080618.pdf

• Cones: LP, SDP

• Installation (Windows): Binary distributions can be obtained from http://sdpa.sourceforge.net/download.html (use the SDPA-M version). Extract binary distribution to arbitrary location and use addpath within MATLAB to add the solver and interface routines.

• Invocation: Call mexsdpa from the Octave or MATLAB command prompt.

• Notes: The “native” installation for Windows and MATLAB is the most reliable. The other three combinations worked partially or not at all. Some of the Linux efforts are reflected in the GitHub repository.

SDPT3

• Website: https://blog.nus.edu.sg/mattohkc/softwares/sdpt3/

• GitHub: https://github.com/sqlp/sdpt3 (preferred) or https://github.com/Kim-ChuanToh/SDPT3

• Documentation: https://blog.nus.edu.sg/mattohkc/files/2019/10/guide4-0-draft.pdf

• Cones: Free variables, LP, SOCP, SDP

• Installation: Download the files from the preferred GitHub repository extracted to an arbitrary location and run install_sdpt3 from the Octave or MATLAB command prompt.

• Invocation: Call sqlp from the Octave or MATLAB command prompt.

• Notes: In case of errors with the MEX-Interface, run install_sdpt3 -rebuild from the Octave or MATLAB command prompt. The SDPT3 function randmat is in conflict with the INTLAB function randmat. To resolve that conflict, we chose to rename the INTLAB function.

SeDuMi

• Website: http://sedumi.ie.lehigh.edu

• GitHub: https://github.com/sqlp/sedumi (preferred)

• Documentation: http://sedumi.ie.lehigh.edu/sedumi/files/sedumi-downloads/SeDuMi_Guide_11.pdf and http://sedumi.ie.lehigh.edu/sedumi/files/sedumi-downloads/usrguide.ps

• Cones: Free variables, LP, SOCP, SDP

• Installation: Download the files from the preferred GitHub repository extracted to an arbitrary location and run install_sedumi from the Octave or MATLAB command prompt.

• Invocation: Call sedumi from the Octave or MATLAB command prompt.

• Notes: In case of errors with the MEX-Interface, run install_sedumi -rebuild from the Octave or MATLAB command prompt.

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