×

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; Benchmarks for Optimization Software; Sparse-BSOS; CSDP; PENNON; PHCpack; LMI toolbox; NCSOStools
Cited in: 374 Documents

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
all top 5

Cited by 502 Authors

38 Lasserre, Jean-Bernard
36 Nie, Jiawang
26 Henrion, Didier
18 Fan, Jinyan
14 Zhou, Anwa
13 Magron, Victor
12 Laurent, Monique
9 Povh, Janez
8 Klep, Igor
8 Zhang, Xinzhen
8 Zhou, Guangming
7 de Klerk, Etienne
7 Qi, Liqun
6 Kojima, Masakazu
6 Parrilo, Pablo A.
6 Tang, Xindong
6 Zhi, Lihong
6 Zhong, Suhan
5 Guo, Feng
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 Korda, Milan
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 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 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 Huang, Lei
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
2 Ma, Yue
...and 402 more Authors
all top 5

Cited in 110 Serials

36 Journal of Global Optimization
32 Mathematical Programming. Series A. Series B
32 SIAM Journal on Optimization
24 Computational Optimization and Applications
16 Automatica
8 Optimization Methods & Software
8 Optimization Letters
7 Journal of Symbolic Computation
6 Journal of the Franklin Institute
6 ACM Transactions on Mathematical Software
6 SIAM Journal on Matrix Analysis and Applications
6 Foundations of Computational Mathematics
5 Journal of Optimization Theory and Applications
5 Journal of Mathematical Imaging and Vision
5 Journal of Industrial and Management Optimization
5 Mathematical Programming Computation
4 International Journal of Control
4 Systems & Control Letters
4 Automation and Remote Control
4 European Journal of Operational Research
4 Linear Algebra and its Applications
3 Archiv der Mathematik
3 Journal of Computational and Applied Mathematics
3 Journal of Pure and Applied Algebra
3 Mathematics of Operations Research
3 Theoretical Computer Science
3 Transactions of the American Mathematical Society
3 Operations Research Letters
3 Journal of Scientific Computing
3 Mathematical Methods of Operations Research
3 Set-Valued and Variational Analysis
3 Numerical Algebra, Control and Optimization
3 SIAM Journal on Applied Algebra and Geometry
2 Mathematical Biosciences
2 Applied Mathematics and Computation
2 Numerische Mathematik
2 Proceedings of the American Mathematical Society
2 SIAM Journal on Control and Optimization
2 Acta Applicandae Mathematicae
2 Discrete & Computational Geometry
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 Mathematical Control and Related Fields
1 American Mathematical Monthly
1 Journal of Mathematical Analysis and Applications
1 Journal of Mathematical Physics
1 Linear and Multilinear Algebra
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 Mathematische Annalen
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 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

290 Operations research, mathematical programming (90-XX)
97 Numerical analysis (65-XX)
52 Systems theory; control (93-XX)
50 Linear and multilinear algebra; matrix theory (15-XX)
46 Algebraic geometry (14-XX)
35 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