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.

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  1. Bonnard, Bernard; Cots, Olivier; Rouot, Jérémy; Verron, Thibaut: Time minimal saturation of a pair of spins and application in magnetic resonance imaging (2020)
  2. Cerone, Vito; Razza, Valentino; Regruto, Diego: One-shot set-membership identification of generalized Hammerstein-Wiener systems (2020)
  3. Cheng, Lulu; Zhang, Xinzhen: A semidefinite relaxation method for second-order cone polynomial complementarity problems (2020)
  4. 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)
  5. Marx, Swann; Weisser, Tillmann; Henrion, Didier; Lasserre, Jean Bernard: A moment approach for entropy solutions to nonlinear hyperbolic PDEs (2020)
  6. Nie, Jiawang; Yang, Liu; Zhong, Suhan: Stochastic polynomial optimization (2020)
  7. van Ackooij, Wim; Pérez-Aros, Pedro: Gradient formulae for nonlinear probabilistic constraints with non-convex quadratic forms (2020)
  8. Wang, Xiao; Zhang, Xinzhen; Zhou, Guangming: SDP relaxation algorithms for (\mathbfP(P_0))-tensor detection (2020)
  9. Wang, Yulei; Gao, Jinwu; Li, Kai; Chen, Hong: Integrated design of control allocation and triple-step control for over-actuated electric ground vehicles with actuator faults (2020)
  10. Zhao, Ruixue; Fan, Jinyan: Higher-degree tensor eigenvalue complementarity problems (2020)
  11. Zhou, Anwa; Fan, Jinyan; Wang, Qingwen: Completely positive tensors in the complex field (2020)
  12. Zhou, Anwa; Fan, Jinyan; Zhou, Guangming: Hermitian completely positive matrices (2020)
  13. Zhou, Guangming; Wang, Qin; Zhao, Wenjie: Saddle points of rational functions (2020)
  14. Chuong, T. D.; Jeyakumar, V.; Li, G.: A new bounded degree hierarchy with SOCP relaxations for global polynomial optimization and conic convex semi-algebraic programs (2019)
  15. De Castro, Yohann; Gamboa, Fabrice; Henrion, Didier; Hess, Roxana; Lasserre, Jean-Bernard: Approximate optimal designs for multivariate polynomial regression (2019)
  16. de Klerk, Etienne; Laurent, Monique: A survey of semidefinite programming approaches to the generalized problem of moments and their error analysis (2019)
  17. Dickinson, Peter J. C.; Povh, Janez: A new approximation hierarchy for polynomial conic optimization (2019)
  18. Dressler, Mareike; Iliman, Sadik; de Wolff, Timo: An approach to constrained polynomial optimization via nonnegative circuit polynomials and geometric programming (2019)
  19. Ito, Naoki; Kim, Sunyoung; Kojima, Masakazu; Takeda, Akiko; Toh, Kim-Chuan: Algorithm 996: BBCPOP: a sparse doubly nonnegative relaxation of polynomial optimization problems with binary, box, and complementarity constraints (2019)
  20. Kussaba, Hugo T. M.; Ishihara, João Y.; Menezes, Leonardo R. A. X.: A robust unscented transformation for uncertain moments (2019)

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