GloptiPoly
GloptiPoly 3 is intended to solve, or at least approximate, the Generalized Problem of Moments (GPM), an infinite-dimensional optimization problem which can be viewed as an extension of the classical problem of moments. From a theoretical viewpoint, the GPM has developments and impact in various areas of mathematics such as algebra, Fourier analysis, functional analysis, operator theory, probability and statistics, to cite a few. In addition, and despite a rather simple and short formulation, the GPM has a large number of important applications in various fields such as optimization, probability, finance, control, signal processing, chemistry, cristallography, tomography, etc.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.
Keywords for this software
References in zbMATH (referenced in 204 articles , 1 standard article )
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Sorted by year (- Friedl, Tobias; Riener, Cordian; Sanyal, Raman: Reflection groups, reflection arrangements, and invariant real varieties (2018)
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- de Klerk, Etienne; Laurent, Monique; Sun, Zhao: Convergence analysis for Lasserre’s measure-based hierarchy of upper bounds for polynomial optimization (2017)
- Fan, Jinyan; Zhou, Anwa: A semidefinite algorithm for completely positive tensor decomposition (2017)
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- Lasserre, Jean B.: Computing Gaussian & exponential measures of semi-algebraic sets (2017)
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- Nie, Jiawang; Wang, Li; Ye, Jane J.: Bilevel polynomial programs and semidefinite relaxation methods (2017)
- Toth, Csaba D. (ed.); Goodman, Jacob E. (ed.); O’Rourke, Joseph (ed.): Handbook of discrete and computational geometry (2017)
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- Boukouvala, Fani; Misener, Ruth; Floudas, Christodoulos A.: Global optimization advances in mixed-integer nonlinear programming, MINLP, and constrained derivative-free optimization, CDFO (2016)
- Bugarin, Florian; Henrion, Didier; Lasserre, Jean Bernard: Minimizing the sum of many rational functions (2016)
- Chen, Yannan; Qi, Liqun; Wang, Qun: Positive semi-definiteness and sum-of-squares property of fourth order four dimensional Hankel tensors (2016)
- Claeys, Mathieu; Daafouz, Jamal; Henrion, Didier: Modal occupation measures and LMI relaxations for nonlinear switched systems control (2016)
- de Klerk, Etienne: Book review of: J.-B. Lasserre, An introduction to polynomial and semi-algebraic optimization (2016)
- Dumitrescu, Bogdan; Şicleru, Bogdan C.; Avram, Florin: Modeling probability densities with sums of exponentials via polynomial approximation (2016)