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.

References in zbMATH (referenced in 185 articles , 1 standard article )

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  1. Chen, Bilian; He, Simai; Li, Zhening; Zhang, Shuzhong: On new classes of nonnegative symmetric tensors (2017)
  2. Claeys, Mathieu; Henrion, Didier; Kružík, Martin: Semi-definite relaxations for optimal control problems with oscillation and concentration effects (2017)
  3. de Klerk, Etienne; Laurent, Monique; Sun, Zhao: Convergence analysis for Lasserre’s measure-based hierarchy of upper bounds for polynomial optimization (2017)
  4. Apkarian, Pierre; Noll, Dominikus; Ravanbod, Laleh: Nonsmooth bundle trust-region algorithm with applications to robust stability (2016)
  5. Boukouvala, Fani; Misener, Ruth; Floudas, Christodoulos A.: Global optimization advances in mixed-integer nonlinear programming, MINLP, and constrained derivative-free optimization, CDFO (2016)
  6. Bugarin, Florian; Henrion, Didier; Lasserre, Jean Bernard: Minimizing the sum of many rational functions (2016)
  7. Chen, Yannan; Qi, Liqun; Wang, Qun: Positive semi-definiteness and sum-of-squares property of fourth order four dimensional Hankel tensors (2016)
  8. Claeys, Mathieu; Daafouz, Jamal; Henrion, Didier: Modal occupation measures and LMI relaxations for nonlinear switched systems control (2016)
  9. de Klerk, Etienne: Book review of: J.-B. Lasserre, An introduction to polynomial and semi-algebraic optimization (2016)
  10. Dumitrescu, Bogdan; Şicleru, Bogdan C.; Avram, Florin: Modeling probability densities with sums of exponentials via polynomial approximation (2016)
  11. Fan, Jinyan; Zhou, Anwa: Computing the distance between the linear matrix pencil and the completely positive cone (2016)
  12. Fan, Jinyan; Zhou, Anwa: The CP-matrix approximation problem (2016)
  13. Grimstad, Bjarne; Sandnes, Anders: Global optimization with spline constraints: a new branch-and-bound method based on B-splines (2016)
  14. Heller, Jan; Pajdla, Tomas: Gposolver: a Matlab/C++ toolbox for global polynomial optimization (2016)
  15. Iliman, Sadik; de Wolff, Timo: Lower bounds for polynomials with simplex Newton polytopes based on geometric programming (2016)
  16. Jeyakumar, V.; Lasserre, J.B.; Li, G.; Phạm, T.S.: Convergent semidefinite programming relaxations for global bilevel polynomial optimization problems (2016)
  17. Klep, Igor; Povh, Janez: Constrained trace-optimization of polynomials in freely noncommuting variables (2016)
  18. Kuntz, Juan; Ottobre, Michela; Stan, Guy-Bart; Barahona, Mauricio: Bounding stationary averages of polynomial diffusions via semidefinite programming (2016)
  19. Le, Thanh Hieu; Van Barel, Marc: A convex optimization model for finding non-negative polynomials (2016)
  20. Ma, Yue; Wang, Chu; Zhi, Lihong: A certificate for semidefinite relaxations in computing positive-dimensional real radical ideals (2016)

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