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| # SCIP-SDP | ||
| A mixed integer semidefinite programming plugin for SCIP | ||
| # SCIP-SDP - A framework for solving mixed-integer semidefinite programs | ||
|
|
||
| This repository provides access to the current release 4.2.0 of | ||
| SCIP-SDP, see the <a | ||
| href="https://wwwopt.mathematik.tu-darmstadt.de/scipsdp/">web page of | ||
| SCIP-SDP</a> for more information and documentation. | ||
| SCIP-SDP is a plugin for SCIP to solve mixed integer semidefinite | ||
| programs (MISDPs), i.e., semidefinite programs (SDPs) in which some | ||
| variables are required to be integral. | ||
|
|
||
| To use the nonlinear branch-and-bound approach, one of the | ||
| following SDP-solvers needs to be installed: | ||
| <ul> | ||
| <li><a href="http://www.mcs.anl.gov/hs/software/DSDP/">DSDP</a></li> | ||
| <li><a href="http://sdpa.sourceforge.net/">SDPA</a></li> | ||
| <li><a href="https://www.mosek.com/">MOSEK</a></li> | ||
| </ul> | ||
| It combines the branch-and-bound framework of SCIP with interior-point | ||
| SDP-solvers to solve MISDPs using either a nonlinear branch-and-bound | ||
| approach or an outer-approximation-based cutting-plane approach using | ||
| linear programs (LPs). In addition to providing a constraint handler | ||
| for SDP-constraints and a relaxator to solve continuous | ||
| SDP-relaxations using interior-point solvers, SCIP-SDP adds several | ||
| heuristics and propagators to SCIP. | ||
|
|
||
| ## Copyright and license | ||
| The MISDPs can be read in using either the CBF-format or an extended | ||
| SDPA-format with support for integrality as well as rank-1 | ||
| constraints. For a description of the extended SDPA-format see the | ||
| file `sdpa_format.txt`. The CBF-format is supported up to version 2, | ||
| see https://cblib.zib.de, and has also been extended to support rank-1 | ||
| constraints. | ||
|
|
||
| Copyright 2011-2013 Discrete Optimization, TU Darmstadt and EDOM, FAU Erlangen-Nürnberg | ||
| 2014-2023 Discrete Optimization, TU Darmstadt | ||
| To use the nonlinear branch-and-bound approach, one of the following | ||
| SDP-solvers needs to be installed: DSDP, SDPA, or MOSEK. For more | ||
| information about the installation of SCIP-SDP see the INSTALL file. | ||
|
|
||
| Licensed under the Apache License, Version 2.0, see [LICENSE](LICENSE). | ||
| ## Features | ||
|
|
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| - SCIP-SDP can read MISDPs in CBF or extended SDPA format. | ||
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| - SCIP-SDP contains presolving and propagation methods as well as primal | ||
| heuristics. | ||
|
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| - SCIP-SDP supports rank-1 constraints by adding quadratic constraints | ||
| for each 2 by 2 minor. Such problems are usually (very) hard to | ||
| solve. | ||
|
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||
| - One can switch between solving SDPs or using an outer approximation | ||
| via LP-relaxations. | ||
|
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| - SCIP-SDP extends SCIP and can be incorporated into other codes | ||
| similar to how this can be done for SCIP. | ||
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| ## Interesting Parameters | ||
|
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||
| SCIP-SDP features many parameters to determine its behavior and it | ||
| inherits all SCIP parameters. Here, we highlight some: | ||
|
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| - `misc/solvesdps`: Determines whether SDPs (1) or LPs (0) are | ||
| solved. It depends on the instance which approach is faster. | ||
|
|
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| - `relaxing/SDP/sdpsolverthreads` sets the number of threads used for | ||
| solving SDPs. By default it is set to 1, since this seems to be the | ||
| fastest for most instances. For larger SDPs it might help to | ||
| increase this number, where a value of -1 corresponds to an | ||
| automatic choice, if this is supported by the SDP solver. | ||
|
|
||
| - Tolerances: `numerics/feastol` and `numerics/dualfeastol` (default | ||
| 1e-5) are SCIP parameters that determine the feasibility | ||
| tolerances. Note that the default is a bit weaker than the default | ||
| SCIP parameter values (1e-6 and 1e-7, respectively). | ||
| `relaxing/SDP/sdpsolverfeastol` and `relaxing/SDP/sdpsolvergaptol` | ||
| (default 1e-5) determine the tolerances used for the SDP-solvers. | ||
| For Mosek the feasibility tolerance is always tightened by 0.1, | ||
| because this generated more reliable results. Depending on the | ||
| instance, changing these parameters might have a dramatic effect on | ||
| performance and correctness of the results (due to numerical | ||
| issues). | ||
|
|
||
| - Slater condition: The solution process of interior-point methods for | ||
| SDPs depends on the Slater condition. One can determine the Slater | ||
| condition for the primal and dual problem by changing | ||
| `relaxing/SDP/slatercheck` (0: no, 1: yes but only for statistics, 2: | ||
| yes and print warning for every problem not satisfying primal and | ||
| dual Slater condition). | ||
|
|
||
| ## Documentation | ||
|
|
||
| - A doxygen documentation is given at | ||
| https://wwwopt.mathematik.tu-darmstadt.de/scipsdp/ . | ||
|
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||
| - Reports for the SCIP Optimization Suites listed at | ||
| https://www.scipopt.org/index.php#cite each contain a part on the | ||
| developments in SCIP-SDP. | ||
|
|
||
| - Many methods used in SCIP-SDP are described in the following dissertations: | ||
|
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||
| Sonja Mars (2013) "Mixed-Integer Semidefinite Programming with an | ||
| Application to Truss Topology Design" | ||
|
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| Tristan Gally (2019) "Computational Mixed-Integer Semidefinite | ||
| Programming" | ||
|
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| Frederic Matter (2022) "Sparse Recovery Under Side Constraints Using | ||
| Null Space Properties" | ||
|
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| ## License | ||
|
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||
| Copyright: | ||
| - 2011-2013 Discrete Optimization, TU Darmstadt and EDOM, FAU Erlangen-Nürnberg | ||
| - 2014- Discrete Optimization, TU Darmstadt | ||
|
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||
| Licensed under the Apache License, Version 2.0 (the "License"), see the `LICENSE` file. | ||
| You may not use this file except in compliance with the License. | ||
| You may obtain a copy of the License at https://www.apache.org/licenses/LICENSE-2.0 . | ||
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||
| Unless required by applicable law or agreed to in writing, software | ||
| distributed under the License is distributed on an "AS IS" BASIS, | ||
| WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. | ||
| See the License for the specific language governing permissions and | ||
| limitations under the License. |