The present version of GloptiPoly 3 can handle moment problems with polynomial data. Many important applications in e.g. optimization, probability, financial economics and optimal control, can be viewed as particular instances of the GPM, and (possibly after some transformation) of the GPM with polynomial data.
The approach is similar to that used in the former version 2 of GloptiPoly. The software allows to build up a hierarchy of semidefinite programming (SDP), or linear matrix inequality (LMI) relaxations of the GPM, whose associated monotone sequence of optimal values converges to the global optimum.
GloptiPoly 3 is described in:
The GPM and its SDP formulation are described in:
It is a freeware subject to the General Public Licence (GPL) policy.
The archive contains an Octave version of gloptipoly3 made with the patch file, tested on Win10/VirtualBox as follows: 1) Octave was downloaded via its Windows installer, 2) SeDuMi was downloaded from github, 3) after installing Octave, SeDuMi was unzipped in the gloptipoly3 directory, 4) the SeDuMi path was added with "addpath('SeDuMi')" and 5) SeDuMi was compiled with the Octave command "install_sedumi". A simple script, inst.m, installing GloptiPoly and running gloptipolydemo.m and the resulting diary file are provided.
Gloptipoly 3.7 benefited from feedback by Milan Korda and Jiawang Nie.
Gloptipoly 3.8 fixes a bug in the YALMIP interface pointed out by Mathieu Claeys.
GloptiPoly 3.9 fixes a bug in the case of no objective function as pointed by Swann Marx, Quentin Vila and Tillmann Weisser.
Gloptipoly 3.10 fixes a bug in the @mpol/subs function as reported by Lu Wang and Eloise Berthier.
The Octave version of GloptiPoly 3.10 was prepared by Robert Jenssen.
Please forward comments, suggestions and bug reports to Didier Henrion.
Last updated on 22 November 2021.