CAQM: Convexity Analysis of Quadratic Maps

Code for various tasks for quadratic maps.

See the paper Geometry of quadratic maps via convex relaxation, Anatoly Dymarsky, Elena Gryazina, Sergei Volodin, Boris Polyak, 2018, arXiv:1810.00896

Prerequisites

• MATLAB (tested with 9.6-2019a) with Parallel Computing toolbox
• CVX. Tested with Version 2.1, Build 1127 (95903bf)
• Tested on Linux (Debian 10.1) amd64 kernel 4.19.0-6-amd64, Java version 1.8.0_181
• Mathematica 12 for semi-analytical tests and figures 4, 7

Installing

See doc/readme.pdf file

Testing

To test separate functions run in MATLAB from root directory:

>> cd tests
>> runtests('testFunctions')

Result should be like the following:

Totals:
   15 Passed, 0 Failed, 0 Incomplete.
   45.7854 seconds testing time.

Moreover, see tests/testCAQM.m as an example of library usage.

>> cd tests
>> testCAQM

Should give output ending with TEST PASSED. A Youtube video demonstrates how the test normally performs.

For more information see doc/readme.pdf

License

See LICENSE.txt

Files and folders

• / -- main functions (see doc/readme.pdf)
• library/ -- supplementary functions (see doc/library.pdf)
• doc/ -- documentation
• examples/ contains the code which reproduces the results from the Section 7. Examples from the article, both using our library (MATLAB) and using semi-analytical methods (Mathematica)
• examples/figures/ -- MATLAB code for drawing figures from the article:
  • example05_c_minus.m reproduces Fig. 5a
  • example05_c_dot_z_c_t_plot.m reproduces Fig. 5b
  • example06_c_minus.m reproduces Fig. 6a
  • example06_c_dot_z_c_t_plot.m reproduces Fig. 6b
  • homogeneous_procedure_H.m reproduces Fig. 8
• examples/ also contains Mathematica notebooks for reproducing Figures 4 and 7: article_example01_fig4.nb and article_example10_fig7.nb
• examples/maps -- sample quadratic maps
• tests/ -- code for testing the setup

Parameters

The library contains several numerical constants the purpose of which is described on the second page of the supplementary functions document doc/library.pdf.

Further reading

Refer to the documentation in doc/readme.pdf and the article

Copyright (c) 2015-2019 Anatoly Dymarsky, Elena Gryazina, Sergei Volodin, Boris Polyak