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 313 articles , 1 standard article )

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  1. Audet, Charles; Hansen, Pierre; Svrtan, Dragutin: Using symbolic calculations to determine largest small polygons (2021)
  2. Buchheim, Christoph; Fampa, Marcia; Sarmiento, Orlando: Lower bounds for cubic optimization over the sphere (2021)
  3. Cheng, Lulu; Zhang, Xinzhen; Ni, Guyan: A semidefinite relaxation method for second-order cone tensor eigenvalue complementarity problems (2021)
  4. Elloumi, Sourour; Lambert, Amélie; Lazare, Arnaud: Solving unconstrained 0-1 polynomial programs through quadratic convex reformulation (2021)
  5. Korda, Milan; Henrion, Didier; Mezić, Igor: Convex computation of extremal invariant measures of nonlinear dynamical systems and Markov processes (2021)
  6. Kuntz, Juan; Thomas, Philipp; Stan, Guy-Bart; Barahona, Mauricio: Approximations of countably infinite linear programs over bounded measure spaces (2021)
  7. Lasserre, Jean B.; Weisser, Tillmann: Distributionally robust polynomial chance-constraints under mixture ambiguity sets (2021)
  8. Lee, Jae Hyoung; Sisarat, Nithirat; Jiao, Liguo: Multi-objective convex polynomial optimization and semidefinite programming relaxations (2021)
  9. Naldi, Simone; Sinn, Rainer: Conic programming: infeasibility certificates and projective geometry (2021)
  10. Nie, Jiawang; Tang, Xindong; Xu, Lingling: The Gauss-Seidel method for generalized Nash equilibrium problems of polynomials (2021)
  11. Sekiguchi, Yoshiyuki; Waki, Hayato: Perturbation analysis of singular semidefinite programs and its applications to control problems (2021)
  12. Wang, Jie; Magron, Victor; Lasserre, Jean-Bernard: TSSOS: a moment-SOS hierarchy that exploits term sparsity (2021)
  13. Wang, Jie; Magron, Victor; Lasserre, Jean-Bernard: Chordal-TSSOS: a moment-SOS hierarchy that exploits term sparsity with chordal extension (2021)
  14. Zeng, Meilan: Tensor (Z)-eigenvalue complementarity problems (2021)
  15. Bonnard, Bernard; Cots, Olivier; Rouot, Jérémy; Verron, Thibaut: Time minimal saturation of a pair of spins and application in magnetic resonance imaging (2020)
  16. Cen, Xiaoli; Xia, Yong: Globally maximizing the sum of squares of quadratic forms over the unit sphere (2020)
  17. Cerone, Vito; Razza, Valentino; Regruto, Diego: One-shot set-membership identification of generalized Hammerstein-Wiener systems (2020)
  18. Cheng, Lulu; Zhang, Xinzhen: A semidefinite relaxation method for second-order cone polynomial complementarity problems (2020)
  19. Fan, Jinyan; Nie, Jiawang; Zhao, Ruixue: The maximum tensor complementarity eigenvalues (2020)
  20. Jarre, Florian; Lieder, Felix; Liu, Ya-Feng; Lu, Cheng: Set-completely-positive representations and cuts for the max-cut polytope and the unit modulus lifting (2020)

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