SDPB(1)

💖 SDPB(1) 💖

okay so bestie, welcome to the User Commands section of the manual, and today's main character is sdpb — the Semidefinite program solver. pull up a chair, grab a strawberry 🍓, and let's get into it.

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✨ NAME ✨

sdpb — Semidefinite program solver

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🦋 SYNOPSIS 🦋

sdpb [OPTIONS] [SOLVER PARAMETERS]

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🌸 DESCRIPTION 🌸

ERROR: the option '--sdpFile' is required but missing

no literally, that's what it says. it's giving "you forgot the one thing that matters" 💀

🎀 Basic options:

• -h, --help — Show this helpful message. (iconic behaviour, honestly)
• -s, --sdpFile arg — SDP data file in XML format. (this is the one you cannot skip, bestie)
• -p, --paramFile arg — Any parameter can optionally be set via this file in key=value format. Command line arguments override values in the parameter file. (cli stays winning 👑)
• -o, --outFile arg — The optimal solution is saved to this file in Mathematica format. Defaults to sdpFile with '.out' extension.
• -c, --checkpointFile arg — Checkpoints are saved to this file every checkpointInterval. Defaults to sdpFile with '.ck' extension.

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💅 Solver parameters:

• --precision arg (=400) — Precision in binary digits. GMP will round up to the nearest multiple of 64 (or 32 on older systems).
• --maxThreads arg (=4) — Maximum number of threads to use for parallel calculation. (parallelism slay)
• --checkpointInterval arg (=3600) — Save checkpoints to checkpointFile every checkpointInterval seconds.
• --noFinalCheckpoint — Don't save a final checkpoint after terminating (useful when debugging).
• --findPrimalFeasible — Terminate once a primal feasible solution is found.
• --findDualFeasible — Terminate once a dual feasible solution is found.
• --detectPrimalFeasibleJump — Terminate if a primal-step of 1 is taken. This often indicates that a primal feasible solution would be found if the precision were high enough. Try increasing either primalErrorThreshold or precision and run from the latest checkpoint.
• --detectDualFeasibleJump — Terminate if a dual-step of 1 is taken. This often indicates that a dual feasible solution would be found if the precision were high enough. Try increasing either dualErrorThreshold or precision and run from the latest checkpoint.
• --maxIterations arg (=500) — Maximum number of iterations to run the solver.
• --maxRuntime arg (=86400) — Maximum amount of time to run the solver in seconds.
• --dualityGapThreshold arg (=1e-30) — Threshold for duality gap (roughly the difference in primal and dual objective) at which the solution is considered optimal. Corresponds to SDPA's epsilonStar.
• --primalErrorThreshold arg (=1e-30) — Threshold for feasibility of the primal problem. Corresponds to SDPA's epsilonBar.
• --dualErrorThreshold arg (=1e-30) — Threshold for feasibility of the dual problem. Corresponds to SDPA's epsilonBar.
• --initialMatrixScalePrimal arg (=1e+20) — The primal matrix X begins at initialMatrixScalePrimal times the identity matrix. Corresponds to SDPA's lambdaStar.
• --initialMatrixScaleDual arg (=1e+20) — The dual matrix Y begins at initialMatrixScaleDual times the identity matrix. Corresponds to SDPA's lambdaStar.
• --feasibleCenteringParameter arg (=0.1) — Shrink the complementarity X Y by this factor when the primal and dual problems are feasible. Corresponds to SDPA's betaStar.
• --infeasibleCenteringParameter arg (=0.3) — Shrink the complementarity X Y by this factor when either the primal or dual problems are infeasible. Corresponds to SDPA's betaBar.
• --stepLengthReduction arg (=0.7) — Shrink each newton step by this factor (smaller means slower, more stable convergence). Corresponds to SDPA's gammaStar.
• --choleskyStabilizeThreshold arg (=1e-40) — Adds stabilizing terms to the cholesky decomposition of the schur complement matrix for diagonal entries which are smaller than this threshold times the geometric mean of other diagonal entries. Somewhat higher choleskyStabilizeThreshold can improve numerical stability but if the threshold is large enough that a high proportion of eigenvalues are being stabilized, the computation will slow substantially. (stability vs speed, the eternal vibe check ⚖️)
• --maxComplementarity arg (=1e+100) — Terminate if the complementarity mu = Tr(X Y)/dim(X) exceeds this value.

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🔥 EXAMPLES 🔥

The example files are contained in the package sdpb-doc and can be found at /usr/share/doc/sdpb-doc/examples/.

The input format for SDPB is XML-based and described in the manual. The Mathematica file mathematica/SDPB.m includes code to export semidefinite programs in this format, along with some examples. An example input file test.xml is included as well.

Two python wrappers for SDPB are also available:

• PyCFTBoot by Connor Behan (arXiv:1602.02810)
• cboot by Tomoki Ohtsuki (arXiv:1602.07295).

wrappers?? we love a good wrapper 🫶

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🌈 SEE ALSO 🌈

The SDPB manual and the README file are contained in the package sdpb-doc and can be found at /usr/share/doc/sdpb-doc/.

The full documentation for sdpb is maintained as a Texinfo manual. If the info and sdpb programs are properly installed at your site, the command

info sdpb

should give you access to the complete manual. (go read it, iykyk 💖)

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💜 AUTHOR 💜

This manpage was written by Nilesh Patra for the Debian distribution and can be used for any other usage of the program.

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and that's the whole thing bestie, no cap. ✨ This is sdpb version 1.0, dated February 2021 — take care of her, she's iconic. 🎀🦋💅