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.


References in zbMATH (referenced in 225 articles , 1 standard article )

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  1. Dressler, Mareike; Iliman, Sadik; de Wolff, Timo: An approach to constrained polynomial optimization via nonnegative circuit polynomials and geometric programming (2019)
  2. Aßmann, Denis; Liers, Frauke; Stingl, Michael; Vera, Juan C.: Deciding robust feasibility and infeasibility using a set containment approach: an application to stationary passive gas network operations (2018)
  3. Bartoli, Adrien; Collins, Toby: Plane-based resection for metric affine cameras (2018)
  4. Chen, Zhongming; Liu, Jinjie; Qi, Liqun; Zheng, Quanshui; Zou, Wennan: An irreducible function basis of isotropic invariants of a third order three-dimensional symmetric tensor (2018)
  5. Deng, Zhibin; Fang, Shu-Cherng; Lu, Cheng; Guo, Xiaoling: A branch-and-cut algorithm using polar cuts for solving nonconvex quadratic programming problems (2018)
  6. Fan, Jinyan; Nie, Jiawang; Zhou, Anwa: Tensor eigenvalue complementarity problems (2018)
  7. Friedl, Tobias; Riener, Cordian; Sanyal, Raman: Reflection groups, reflection arrangements, and invariant real varieties (2018)
  8. Josz, Cédric; Molzahn, Daniel K.: Lasserre hierarchy for large scale polynomial optimization in real and complex variables (2018)
  9. L^e, C^ong-Trình; Du, Thị-Hòa-Bình: Handelman’s positivstellensatz for polynomial matrices positive definite on polyhedra (2018)
  10. Nie, Jiawang; Yang, Zi; Zhang, Xinzhen: A complete semidefinite algorithm for detecting copositive matrices and tensors (2018)
  11. Sobrie, Olivier; Gillis, Nicolas; Mousseau, Vincent; Pirlot, Marc: UTA-poly and UTA-splines: additive value functions with polynomial marginals (2018)
  12. Steger, Carsten: Algorithms for the orthographic-$n$-point problem (2018)
  13. Weisser, Tillmann; Lasserre, Jean B.; Toh, Kim-Chuan: Sparse-BSOS: a bounded degree SOS hierarchy for large scale polynomial optimization with sparsity (2018)
  14. Zhou, Anwa; Fan, Jinyan: Completely positive tensor recovery with minimal nuclear value (2018)
  15. Zhou, Anwa; Zhao, Xin; Fan, Jinyan; Bai, Yanqin: Tensor maximal correlation problems (2018)
  16. Buchheim, Christoph; D’Ambrosio, Claudia: Monomial-wise optimal separable underestimators for mixed-integer polynomial optimization (2017)
  17. Chen, Bilian; He, Simai; Li, Zhening; Zhang, Shuzhong: On new classes of nonnegative symmetric tensors (2017)
  18. Claeys, Mathieu; Henrion, Didier; Kružík, Martin: Semi-definite relaxations for optimal control problems with oscillation and concentration effects (2017)
  19. de Klerk, Etienne; Laurent, Monique; Sun, Zhao: Convergence analysis for Lasserre’s measure-based hierarchy of upper bounds for polynomial optimization (2017)
  20. Fan, Jinyan; Zhou, Anwa: A semidefinite algorithm for completely positive tensor decomposition (2017)

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