GloptiPoly swMATH ID: 4343 Software Authors: Henrion, Didier; Lasserre, Jean-Bernard; Loefberg, Johan Description: 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. Homepage: http://homepages.laas.fr/henrion/software/gloptipoly3/ Dependencies: Matlab Keywords: 3- moments; optimization and semidefinite programming Related Software: SeDuMi; YALMIP; Sostools; SDPT3; Matlab; SparsePOP; Mosek; SDPA; TSSOS; CVX; SPOTless; Robotics; BARON; Sparse-BSOS; Benchmarks for Optimization Software; CSDP; PHCpack; PENNON; LMI toolbox; GitHub Cited in: 377 Documents Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year Detecting global optimality and extracting solutions in GloptiPoly. Zbl 1119.93301Henrion, Didier; Lassere, Jean-Bernard 2005 all top 5 Cited by 503 Authors 50 Lasserre, Jean-Bernard 38 Nie, Jiawang 27 Henrion, Didier 18 Fan, Jinyan 14 Magron, Victor 14 Zhou, Anwa 12 Laurent, Monique 9 Povh, Janez 8 Klep, Igor 8 Zhang, Xinzhen 8 Zhou, Guangming 7 de Klerk, Etienne 7 Qi, Liqun 7 Zhong, Suhan 6 Kojima, Masakazu 6 Parrilo, Pablo A. 6 Tang, Xindong 6 Zhi, Lihong 5 Guo, Feng 5 Korda, Milan 5 Nataraj, Paluri S. V. 5 Toh, Kim Chuan 5 Zhang, Shuzhong 4 Cerone, Vito 4 Claeys, Mathieu 4 Demmel, James Weldon 4 Dressler, Mareike 4 He, Simai 4 Huang, Zheng-Hai 4 Jiao, Liguo 4 Kim, Sunyoung 4 Li, Guoyin 4 Li, Zhening 4 Meziat, René J. 4 Parpas, Panos 4 Pozdyaev, V. V. 4 Regruto, Diego 4 Waki, Hayato 4 Wang, Jie 4 Wang, Li 4 Weißer, Tillmann 4 Yang, Zi 3 Bertsimas, Dimitris John 3 Bingane, Christian 3 Bonnard, Bernard 3 Cafuta, Kristijan 3 Chesi, Graziano 3 Dumitrescu, Bogdan Alexandru 3 Huang, Lei 3 Jeyakumar, Vaithilingam 3 Muramatsu, Masakazu 3 Nguang, Sing Kiong 3 Ni, Guyan 3 Nohadani, Omid 3 Oliveira, Ricardo C. L. F. 3 Papp, Dávid 3 Patiño, Diego 3 Peres, Pedro L. D. 3 Piga, Dario 3 Rustem, Berc 3 Saat, Shakir 3 Scherer, Carsten W. 3 Schweighofer, Markus 3 Tacchi, Matteo 3 Van Ackooij, Wim 3 Wang, Qun 3 Yuan, Ya-xiang 3 Zhao, Ruixue 3 Zhao, Wenjie 2 Anjos, Miguel F. 2 Arounassalame, M. 2 Audet, Charles 2 Barahona, Mauricio 2 Bartoli, Adrien 2 Buchheim, Christoph 2 Bugarin, Florian 2 Chen, Bilian 2 Chen, Borsen 2 Chen, Po-Wei 2 Chen, Yannan 2 Chen, Zhongming 2 Cheng, Lulu 2 Cots, Olivier 2 de Wolff, Timo 2 Fialkow, Lawrence A. 2 Floudas, Christodoulos Achilleus 2 Gawali, Deepak D. 2 Goldfarb, Donald 2 Greuet, Aurélien 2 Helton, John William 2 Hsu, Daniel 2 Hu, ShengLong 2 Iliman, Sadik 2 Jibetean, Dorina 2 Josz, Cédric 2 Kawai, Reiichiro 2 Kuntz, Juan 2 Lee, Jae Hyoung 2 Li, Bin 2 Lu, Cheng ...and 403 more Authors all top 5 Cited in 110 Serials 36 Journal of Global Optimization 34 SIAM Journal on Optimization 32 Mathematical Programming. Series A. 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Mathematical Models & Methods in Applied Sciences 1 Numerical Algorithms 1 Applied Mathematical Modelling 1 Communications in Statistics. Simulation and Computation 1 SIAM Review 1 International Journal of Robust and Nonlinear Control 1 Journal of Nonlinear Science 1 Archives of Control Sciences 1 SIAM Journal on Scientific Computing 1 Top 1 Advances in Computational Mathematics 1 Reliable Computing 1 Mathematical Problems in Engineering 1 Mathematical Population Studies 1 Mathematical Finance 1 Positivity 1 New Journal of Physics 1 Optimization and Engineering 1 Nieuw Archief voor Wiskunde. Vijfde Serie 1 Advances in Geometry 1 Discrete and Continuous Dynamical Systems. Series B 1 Journal of Systems Science and Complexity 1 North American Actuarial Journal 1 Discrete Optimization 1 Pacific Journal of Optimization 1 Fields Institute Monographs 1 Frontiers of Mathematics in China 1 Quantum Information & Computation 1 Applied and Computational Mathematics ...and 10 more Serials all top 5 Cited in 40 Fields 292 Operations research, mathematical programming (90-XX) 99 Numerical analysis (65-XX) 53 Systems theory; control (93-XX) 50 Linear and multilinear algebra; matrix theory (15-XX) 46 Algebraic geometry (14-XX) 36 Calculus of variations and optimal control; optimization (49-XX) 28 Computer science (68-XX) 22 Commutative algebra (13-XX) 20 Integral transforms, operational calculus (44-XX) 16 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 15 Operator theory (47-XX) 12 Convex and discrete geometry (52-XX) 11 Field theory and polynomials (12-XX) 10 Measure and integration (28-XX) 9 Number theory (11-XX) 9 Statistics (62-XX) 8 Ordinary differential equations (34-XX) 8 Biology and other natural sciences (92-XX) 6 Geometry (51-XX) 6 Information and communication theory, circuits (94-XX) 5 Partial differential equations (35-XX) 5 Dynamical systems and ergodic theory (37-XX) 4 Approximations and expansions (41-XX) 4 Functional analysis (46-XX) 4 Probability theory and stochastic processes (60-XX) 4 Quantum theory (81-XX) 3 Combinatorics (05-XX) 3 General algebraic systems (08-XX) 3 Functions of a complex variable (30-XX) 2 Real functions (26-XX) 2 Mechanics of deformable solids (74-XX) 2 Optics, electromagnetic theory (78-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Group theory and generalizations (20-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Abstract harmonic analysis (43-XX) 1 Differential geometry (53-XX) 1 Mechanics of particles and systems (70-XX) 1 Statistical mechanics, structure of matter (82-XX) Citations by Year