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fminsearch

swMATH ID: 7467
Software Authors: Lagarias, Jeffrey C.; Reeds, James A.; Wright, Margaret H.; Wright, Paul E.
Description: Convergence properties of the Nelder–Mead simplex method in low dimensions The Nelder–Mead simplex algorithm, first published in 1965, is an enormously popular direct search method for multidimensional unconstrained minimization. Despite its widespread use, essentially no theoretical results have been proved explicitly for the Nelder–Mead algorithm. This paper presents convergence properties of the Nelder–Mead algorithm applied to strictly convex functions in dimensions 1 and 2. We prove convergence to a minimizer for dimension 1, and various limited convergence results for dimension 2. A counterexample of McKinnon gives a family of strictly convex functions in two dimensions and a set of initial conditions for which the Nelder–Mead algorithm converges to a nonminimizer. It is not yet known whether the Nelder–Mead method can be proved to converge to a minimizer for a more specialized class of convex functions in two dimensions.
Homepage: http://www.mathworks.de/de/help/matlab/ref/fminsearch.html
Dependencies: Matlab
Keywords: direct search methods; Nelder-Mead simplex methods; nonderivative optimization
Related Software: Matlab; KELLEY; minpack; BRENT; MultiMin; MATLAB ODE suite; CMA-ES; UOBYQA; NOMAD; PSwarm; IMFIL; DFO; EGO; UCI-ml; ode23s; ode113; Ode15s; ode45; ode23; Genocop
Cited in: 266 Publications
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Cited by 695 Authors

13 Klein, Christian
5 Grava, Tamara
3 Bűrmen, Árpád
3 Das, Ranjan Kumar
3 Dubrovin, Boris Anatol’evich
3 Hwang, Yi-Ting
3 Kuang, Yang
3 Wang, Chun-Chao
3 Weng, Tzu-Chun
2 Ban, Jaepil
2 Banks, Harvey Thomas
2 Chatzis, Sotirios P.
2 Chen, Cheng-Kang
2 Cottereau, Régis
2 Hansen, Pierre
2 Hung, Ta-Wei
2 Jaranowski, Piotr
2 Kaya, C. Yalçin
2 Kim, Sangwoo
2 King, John Robert
2 Królak, Andrzej
2 Lewis, Robert Michael
2 Mladenović, Nenad
2 Neumaier, Arnold
2 Peter, Ralf
2 Puhan, Janez
2 Sahinidis, Nikolaos V.
2 Saut, Jean-Claude
2 Shekari Beidokhti, R.
2 Torczon, Virginia J.
2 Tseng, Paul
2 Tuma, Tadej
2 Witteveen, Jeroen A. S.
2 Wright, Margaret H.
2 Wu, Zhengxiao
1 Abbiati, Roberto Andrea
1 Abdel-Mottaleb, Mohamed
1 Abdussalam, Shehu S.
1 Abel, Steven A.
1 Adanu, Kwami
1 Adnet, Frédéric
1 Ahi, Emrah
1 Ahookhosh, Masoud
1 Akaho, Shotaro
1 Akgiray, Vedat
1 Akian, Marianne
1 Al-Subaihi, Ibrahim A.
1 Alata, Olivier
1 Albrecht, Gudrun
1 Alexandrescu, Diana-Olimpia
1 Alibert, Jean-Jacques
1 Alkhalifa, Loay
1 Allamigeon, Xavier
1 Aloise, Daniel
1 Alonso, María C.
1 Alvarez-Vázquez, Lino Jose
1 Amanbek, Yerlan
1 Andreasen, Martin Møller
1 Andrews, Beth
1 Antonietti, Paola Francesca
1 Aretz-Nellesen, Nicole
1 Audet, Charles
1 Auer, Ekaterina
1 Auger, Anne
1 Auzinger, Günter
1 Ávalos, Edgar
1 Axelrod, David E.
1 Babineau, David
1 Bäck, Thomas H. W.
1 Baeyens, Enrique
1 Bailly, Christian
1 Balakrishnan, Narayanaswamy
1 Bangham, J. Andrew
1 Banjai, Lehel
1 Barlow, Martin T.
1 Barnes, J. H.
1 Barrack, Duncan S.
1 Barrena, Manuel
1 Barrowes, Benjamin E.
1 Bartz-Beielstein, Thomas
1 Basel, Türker
1 Battista, Antonio
1 Berger, Martijn P. F.
1 Berres, Stefan
1 Bettencourt, Luís M. A.
1 Betti, Raimondo
1 Beyder, Arthur
1 Beyer, Hans-Georg
1 Bhowmik, Arka
1 Bientinesi, Paolo
1 Bijl, Hester
1 Birrell, Jeremiah
1 Biscari, Paolo
1 Bishara, Dana
1 Blackmore, Denis L.
1 Blair, Jessica M. A.
1 Bliman, Pierre-Alexandre
1 Blondin, Maude Josée
1 Bobál, Vladimír
1 Boem, Francesca
...and 595 more Authors
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Cited in 136 Serials

11 Journal of Theoretical Biology
8 Applied Mathematical Modelling
8 Computational Optimization and Applications
7 Applied Mathematics and Computation
7 Journal of Computational and Applied Mathematics
7 Pattern Recognition
6 European Journal of Operational Research
6 Computational Statistics and Data Analysis
6 SIAM Journal on Optimization
5 Journal of Mathematical Biology
5 Bulletin of Mathematical Biology
5 Journal of Global Optimization
4 Computer Methods in Applied Mechanics and Engineering
4 Mathematical Biosciences
4 Automatica
4 Journal of Optimization Theory and Applications
4 Mathematics and Computers in Simulation
4 Physica D
4 Computational Mechanics
4 Mathematical Biosciences and Engineering
3 Computers & Mathematics with Applications
3 Journal of the Franklin Institute
3 Journal of Nonlinear Science
3 Computational Economics
3 SIAM Journal on Scientific Computing
3 Journal of Applied Statistics
3 Statistics and Computing
2 Inverse Problems
2 Journal of Computational Physics
2 Physica A
2 Biometrics
2 International Journal for Numerical Methods in Engineering
2 Computers & Operations Research
2 Annals of Operations Research
2 Journal of Statistical Computation and Simulation
2 Test
2 Top
2 Living Reviews in Relativity
2 Structural and Multidisciplinary Optimization
2 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
2 Inverse Problems in Science and Engineering
2 Optimization Letters
2 Statistics and Its Interface
2 Algorithms
1 Biological Cybernetics
1 The Canadian Journal of Statistics
1 Communications on Pure and Applied Mathematics
1 International Journal of Engineering Science
1 International Journal of Heat and Mass Transfer
1 Journal of Fluid Mechanics
1 Metrika
1 Nonlinearity
1 Physics Reports
1 ZAMP. Zeitschrift für angewandte Mathematik und Physik
1 Annals of the Institute of Statistical Mathematics
1 The Annals of Statistics
1 Fuzzy Sets and Systems
1 Hiroshima Mathematical Journal
1 Information Sciences
1 Journal of Mathematical Psychology
1 Journal of Statistical Planning and Inference
1 Mathematische Zeitschrift
1 Meccanica
1 Operations Research
1 Quarterly of Applied Mathematics
1 Studies in Applied Mathematics
1 Topology and its Applications
1 Applied Mathematics and Mechanics. (English Edition)
1 Computer Aided Geometric Design
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1 Statistics
1 Journal of Economic Dynamics & Control
1 Queueing Systems
1 Journal of Scientific Computing
1 European Journal of Applied Mathematics
1 Signal Processing
1 Neural Computation
1 Japan Journal of Industrial and Applied Mathematics
1 IEEE Transactions on Signal Processing
1 International Journal of Adaptive Control and Signal Processing
1 Numerical Algorithms
1 Computational Mathematics and Mathematical Physics
1 YUJOR. Yugoslav Journal of Operations Research
1 Communications in Statistics. Simulation and Computation
1 Journal of Non-Newtonian Fluid Mechanics
1 SIAM Journal on Applied Mathematics
1 SIAM Review
1 Journal of Dynamics and Differential Equations
1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
1 Cybernetics and Systems Analysis
1 Computational and Applied Mathematics
1 Advances in Computational Mathematics
1 Engineering Analysis with Boundary Elements
1 Journal of Difference Equations and Applications
1 Bernoulli
1 Discrete and Continuous Dynamical Systems
1 Journal of Mathematical Chemistry
1 Mathematical Problems in Engineering
1 Mathematics and Mechanics of Solids
1 Mathematical Communications
...and 36 more Serials
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Cited in 37 Fields

80 Operations research, mathematical programming (90-XX)
72 Numerical analysis (65-XX)
53 Statistics (62-XX)
49 Biology and other natural sciences (92-XX)
31 Partial differential equations (35-XX)
24 Computer science (68-XX)
21 Mechanics of deformable solids (74-XX)
21 Systems theory; control (93-XX)
16 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
11 Ordinary differential equations (34-XX)
10 Calculus of variations and optimal control; optimization (49-XX)
10 Probability theory and stochastic processes (60-XX)
7 Fluid mechanics (76-XX)
6 Dynamical systems and ergodic theory (37-XX)
6 Classical thermodynamics, heat transfer (80-XX)
6 Quantum theory (81-XX)
6 Statistical mechanics, structure of matter (82-XX)
5 Optics, electromagnetic theory (78-XX)
5 Information and communication theory, circuits (94-XX)
4 Geophysics (86-XX)
3 Linear and multilinear algebra; matrix theory (15-XX)
3 Relativity and gravitational theory (83-XX)
2 Convex and discrete geometry (52-XX)
2 Global analysis, analysis on manifolds (58-XX)
1 General and overarching topics; collections (00-XX)
1 Combinatorics (05-XX)
1 Order, lattices, ordered algebraic structures (06-XX)
1 Algebraic geometry (14-XX)
1 Measure and integration (28-XX)
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1 Approximations and expansions (41-XX)
1 Integral equations (45-XX)
1 Operator theory (47-XX)
1 Differential geometry (53-XX)
1 Manifolds and cell complexes (57-XX)

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