## GloptiPoly

 swMATH ID: 4343 Software Authors: Didier Henrion; Jean-Bernard Lasserre; Johan Loefberg 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; SDPA; Mosek; CVX; SPOTless; BARON; Sparse-BSOS; Benchmarks for Optimization Software; CSDP; Robotics; LMI toolbox; PENNON; PHCpack; TSSOS; ISOLATE Cited in: 330 Publications

### Standard Articles

1 Publication describing the Software, including 1 Publication in zbMATH Year
Detecting global optimality and extracting solutions in GloptiPoly. Zbl 1119.93301
Henrion, Didier; Lassere, Jean-Bernard
2005
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### Cited by 454 Authors

 46 Lasserre, Jean-Bernard 28 Nie, Jiawang 23 Henrion, Didier 16 Fan, Jinyan 13 Zhou, Anwa 11 Laurent, Monique 8 Magron, Victor 8 Povh, Janez 8 Zhang, Xinzhen 7 de Klerk, Etienne 7 Klep, Igor 6 Kojima, Masakazu 6 Parrilo, Pablo A. 6 Qi, Liqun 6 Zhou, Guangming 5 Nataraj, Paluri S. V. 5 Zhang, Shuzhong 5 Zhi, Lihong 4 Cerone, Vito 4 Claeys, Mathieu 4 Demmel, James Weldon 4 Guo, Feng 4 He, Simai 4 Kim, Sunyoung 4 Li, Guoyin 4 Li, Zhening 4 Meziat, René J. 4 Parpas, Panos 4 Pozdyaev, V. V. 4 Regruto, Diego 4 Toh, Kim Chuan 4 Waki, Hayato 4 Wang, Li 3 Bertsimas, Dimitris John 3 Bonnard, Bernard 3 Cafuta, Kristijan 3 Chesi, Graziano 3 Dumitrescu, Bogdan Alexandru 3 Jeyakumar, Vaithilingam 3 Korda, Milan 3 Muramatsu, Masakazu 3 Nguang, Sing Kiong 3 Nohadani, Omid 3 Patiño, Diego 3 Piga, Dario 3 Rustem, Berc 3 Saat, Shakir 3 Scherer, Carsten W. 3 Schweighofer, Markus 3 Van Ackooij, Wim 3 Wang, Qun 3 Weißer, Tillmann 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 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 Iliman, Sadik 2 Jiao, Liguo 2 Jibetean, Dorina 2 Josz, Cédric 2 Kawai, Reiichiro 2 Kuntz, Juan 2 Li, Bin 2 Lu, Cheng 2 Ma, Yue 2 Mehrotra, Sanjay 2 Messine, Frédéric 2 Misener, Ruth 2 Mu, Cun 2 Ni, Guyan 2 Oliveira, Ricardo C. L. F. 2 Papachristodoulou, Antonis 2 Papp, Dávid 2 Peres, Pedro L. D. 2 Rostalski, Philipp 2 Rouot, Jérémy 2 Safey El Din, Mohab 2 Şicleru, Bogdan C. 2 Song, Xinyu 2 Stan, Guy-Bart 2 Suo, Yaohong 2 Teo, Kwong Meng 2 Thanh, Tung Phan ...and 354 more Authors
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### Cited in 103 Serials

 31 Journal of Global Optimization 28 Mathematical Programming. Series A. Series B 28 SIAM Journal on Optimization 23 Computational Optimization and Applications 15 Automatica 8 Optimization Methods & Software 6 Journal of the Franklin Institute 6 Journal of Symbolic Computation 6 Optimization Letters 5 Journal of Mathematical Imaging and Vision 4 International Journal of Control 4 ACM Transactions on Mathematical Software 4 Journal of Optimization Theory and Applications 4 SIAM Journal on Matrix Analysis and Applications 4 Automation and Remote Control 4 European Journal of Operational Research 4 Linear Algebra and its Applications 4 Foundations of Computational Mathematics 4 Mathematical Programming Computation 3 Archiv der Mathematik 3 Journal of Computational and Applied Mathematics 3 Journal of Pure and Applied Algebra 3 Theoretical Computer Science 3 Systems & Control Letters 3 Operations Research Letters 3 Mathematical Methods of Operations Research 3 Journal of Industrial and Management Optimization 3 Set-Valued and Variational Analysis 2 Mathematical Biosciences 2 Applied Mathematics and Computation 2 Mathematics of Operations Research 2 Proceedings of the American Mathematical Society 2 SIAM Journal on Control and Optimization 2 Transactions of the American Mathematical Society 2 Acta Applicandae Mathematicae 2 Numerical Linear Algebra with Applications 2 International Journal of Computer Vision 2 INFORMS Journal on Computing 2 European Journal of Control 2 RAIRO. Operations Research 2 Science China. Mathematics 2 Numerical Algebra, Control and Optimization 2 Mathematical Control and Related Fields 2 SIAM Journal on Applied Algebra and Geometry 1 American Mathematical Monthly 1 Journal of Mathematical Analysis and Applications 1 Journal of Mathematical Physics 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Mathematics of Computation 1 The Annals of Statistics 1 Applied Mathematics and Optimization 1 Fuzzy Sets and Systems 1 International Journal of Circuit Theory and Applications 1 Journal of Functional Analysis 1 Journal of the Operations Research Society of Japan 1 Mathematics and Computers in Simulation 1 Numerical Functional Analysis and Optimization 1 Operations Research 1 Opsearch 1 Advances in Applied Mathematics 1 Applied Numerical Mathematics 1 Optimization 1 Journal of Complexity 1 Computers & Operations Research 1 International Journal of Adaptive Control and Signal Processing 1 M$$^3$$AS. 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 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 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 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 1 Imperial College Press Optimization Series 1 Asian Journal of Control 1 Statistics and Computing 1 EURO Journal on Computational Optimization 1 Journal of the Operations Research Society of China 1 Signals and Communication Technology ...and 3 more Serials
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### Cited in 39 Fields

 257 Operations research, mathematical programming (90-XX) 80 Numerical analysis (65-XX) 50 Systems theory; control (93-XX) 43 Linear and multilinear algebra; matrix theory (15-XX) 39 Algebraic geometry (14-XX) 30 Calculus of variations and optimal control; optimization (49-XX) 28 Computer science (68-XX) 20 Commutative algebra (13-XX) 19 Integral transforms, operational calculus (44-XX) 12 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 11 Operator theory (47-XX) 10 Field theory and polynomials (12-XX) 9 Number theory (11-XX) 8 Ordinary differential equations (34-XX) 8 Convex and discrete geometry (52-XX) 8 Statistics (62-XX) 8 Biology and other natural sciences (92-XX) 7 Information and communication theory, circuits (94-XX) 6 Measure and integration (28-XX) 5 Dynamical systems and ergodic theory (37-XX) 4 Functional analysis (46-XX) 4 Geometry (51-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) 3 Partial differential equations (35-XX) 3 Approximations and expansions (41-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 Mechanics of particles and systems (70-XX) 1 Statistical mechanics, structure of matter (82-XX)