Libraries for semidefinite approximations of Pareto curves and images of semialgebraic sets
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README.md

README.md

ParetoImageSDP

ParetoImageSDP is a set of libraries using the Yalmip and Gloptipoly toolboxes for MATLAB. It provides functions to compute semidefinite approximations of

  1. Pareto curves (see paretosdp/) implementing the three methods described in: Victor Magron, Didier Henrion and Jean-Bernard Lasserre “Approximating Pareto curves using semidefinite relaxations” (on the arxiv)

  2. Images of semialgebraic sets under polynomial applications (see imagesdp/) implementing the two methods described in Victor Magron, Didier Henrion and Jean-Bernard Lasserre “Semidefinite approximations of projections and polynomial images of semialgebraic sets” (on Optimization Online)

Requirements

Matlab

Gloptipoly Download

Yalmip Download

Mosek Download

Documentation

See

  1. paretosdp/examples/ex11_4.m and paretosdp/examples/test4.m

  2. imagesdp/exists/ex11_4_exists.m

for some example-based documentation.

Warning

This is a preliminary implementation and the probability of finding bugs is high.

Do not hesitate to submit bug report of pull requests.

License

ParetoImageSDP is released under the terms of CeCILL license. This license is compatible with the GNU GPL license.

See the files LICENSE.en or LICENCE.fr for more information.