Stochastic global optimization methods part I: Clustering methods
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Rinnooy Kan and Timmer theoretically proved that a stochastic optimization method converges to the global optimum with probability 1.0 when the number of function evaluations is increased infinitely.
“Rinnooy Kan and Timmer (1987) theoretically proved that a stochastic optimization method converges to the global optimum with probability 1.0 when the number of function evaluations is increased infinitely.”
From Robust 3D–2D image registration: application to spine interventions and vertebral labeling in the presence of anatomical deformation (2013) · cites this paper as Rinnooy Kan and Timmer (1987)
Theorem 1 in the Pure Random Search section proves that the lowest function value found converges almost surely to the global minimum value as the uniform sample size increases. The claim omits the theorem’s conditions, including continuity of the objective function, and says the method converges to the global optimum rather than specifying convergence of its best function value. (LLM, conf=0.84)
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Cites
Simulation and the Monte Carlo Method
Rubinstein, R. Y., & Kroese, D. P. (2016) · Wiley Series in Probability and Statistics · doi:10.1002/9781118631980 · Cited by 3,356 · cited 1× · see citing works
“Proposition 1 (Rubinstein, 1981; cf. Devroye, 1978).”
Flagged first, then by citations
Research works printed but not linked: 19
- Anderssen, R.S. (1972), Global optimization . In R.S. Anderssen, L.S. Jennings and D.M. Ryan (eds.), Optimization (University of Queensland Press).
- Anderssen, R.S. and P. Bloomfield (1975), Properties of the random search in global optimization . Journal of gptimization Theory and Applications 16, 383-398.
- Bahadur, R.R. (1966), A note on quantiles in large samples. Annals of Mathematical Statistics 37, 577-580.
- Becker, R.W. and G.V. Lago (1970), A global optimization algorithm. In Proceedings of the 8th Allerton Conference on Circuits and Systems ,Theory.
- Boender, C.G.E., A.H.G. Rinnooy Kan, L. Stougie and G.T. Timmer (1980), Global optimization : a stochastic approach. In F. Archetti and M. Cugiani (eds.), Numerical Techniques for Stochastic Systems (North- Holland, Amsterdam).
- Boender, C.G.E. (1984), The Generalized Multinomial Distribution : AlLatE1211 .22222212E LLELLEELLE E : Ph.D. Dissertation , Erasmus Universiteit Rotterdam (Centrum voor Wiskunde en Informatica, Amsterdam).
- Boender, C.G.E., Rinnooy Kan and G.T. Timmer (1985), 'A stochastic approach to global optimization To appear in Proceedings of the NATO ASI on Computational Mathematical Programming, Bad Windsheim.
- Chung, K.L. (1974), A course in Probability Theory (Academic Press, London).
- Dixon, L.C.W. and G.P. Szego (eds.) (1975), Towards Global Optimization (North-Holland, Amsterdam).
- Dixon, L.C.W. and G.P. Szego (eds.) (1978a), Towards Global Optimization 2 (North-Holland, Amsterdam).
- Erdos, P. and J. Spencer (1974), Probabilistic Methods in Combinatorics (Academic Press, London).
- Hartman, J.K. (1973), Some experiments in global optimization. Naval Research Lnistics Quarterly 20, 569-576.
- Parzen, E. (1962), On estimation of a probability density functions and mode. Annals of Mathematical Statistics 33, 1065-1076.
- Rinnooy Kan, A.H.G. and G.T. Timmer (1984), Stochastic methods for global optimization. To appear in the American Journal of Mathematical and Management Sciences.
- Ruygrok, A.J. (1982), Mode Analysis in Globaal Optimaliseren. Master Thesis, Erasmus University, Rotterdam (in Dutch).
- Torn, A.A. (1976), Cluster analysis using seed points and density determined hyperspheres with an application to global optimization. In Proceeding of the third International Conference on Pattern Recognition, Coronado, California.
- Wishart, D. (1969), Mode Analysis: a generalization of nearest neighbour which reduces chaining effects. In A.J. Cole (ed.), Numerical Taxonomy (Academic Press, New York).
- Wolfe, P. (1969), Convergence conditions for ascent methods. Siam Review 11 226-235.
- Wolfe, P. (1971), Convergence conditions for ascent methods II: some corrections. Siam Review 13# 185-188.
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Moles, C. G., Mendes, P., & Banga, J. R. (2003) · Genome Research · doi:10.1101/gr.1262503 · Cited by 858 · see citing works
Multistart Methods for Quantum Approximate optimization
Shaydulin, R., Safro, I., & Larson, J. (2019) · 2019 IEEE High Performance Extreme Computing Conference (HPEC) · doi:10.1109/hpec.2019.8916288 · Cited by 110 · see citing works
Otake, Y., Wang, A. S., Webster Stayman, J., Uneri, A., Kleinszig, G., Vogt, S., Khanna, A. J., Gokaslan, Z. L., & Siewerdsen, J. H. (2013) · Physics in Medicine and Biology · doi:10.1088/0031-9155/58/23/8535 · Cited by 85 · see citing works
“Rinnooy Kan and Timmer (1987) theoretically proved that a stochastic optimization method converges to the global optimum with probability 1.0 when the number of function evaluations is increased infinitely.”
MethodInfluential
- Authors
- Rinnooy Kan, A. H. G., & Timmer, G. T.
- Affiliations
- Erasmus University Rotterdam (NL)
- Venue
- Mathematical Programming
- Published
- 1987-09
- Volume
- 39
- Issue
- 1
- Pages
- 27-56
- ISSN
- 0025-5610 (ISSN-L)
- 1436-4646
- OpenAlex
- W1969144558
- Cited by
- 463
- References
- 1
- Citations by year
- 2026: 4 · 2025: 7 · 2024: 13 · 2023: 11 · 2022: 13 · 2021: 18 · 2020: 11 · 2019: 12 · 2018: 19 · 2017: 14 · 2016: 15 · 2015: 15 · 2014: 12 · 2013: 26 · 2012: 9
- FWCI
- 4.93
- Type
- journal article
- Language
- en
- Open access
- green
- ageconsearch.umn.edu
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Mathematical Programming (publishedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- AgEcon Search (University of Minnesota, USA) (submittedVersion, cc-by-nc-nd)
- AgEcon Search (University of Minnesota, USA)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Metaheuristic Optimization Algorithms Research
- Physical Sciences › Mathematics › Numerical Analysis › Advanced Optimization Algorithms Research
- Physical Sciences › Computer Science › Artificial Intelligence › Advanced Clustering Algorithms Research
- Keywords
- stochastic global optimization, clustering algorithms, global minimum
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