Advanced search
Publication Cover
American Journal of Mathematical and Management Sciences Volume 4, 1984 - Issue 1-2: Statistics and Optimization: The Interface
Submit an article Journal homepage
49
Views
36
CrossRef citations to date
0
Altmetric
Original Articles

Stochastic Methods for Global Optimization

A.H.G. Rinnooy KanErasmus University Rotterdam, The Netherlands
&
G.T. TimmerErasmus University Rotterdam, The Netherlands
Pages 7-40 | Published online: 14 Aug 2013

  • AnderssenR.S. (1972). Global optimization. In AnderssenR.S., JenningsL.S. and RyanD.M. (Editors). Optimization. University of Queensland Press.
  • ArchettiF. (1975). A sampling technique for global optimization. In DixonL.C.W. and SzegöG.P. (Editors), Towards Global Optimization. North–Holland, Amsterdam.
  • ArchettiF. and BetroB. (1975). Recursive stochastic evaluation of the level sets measure in global optimization problems. Technical Report. University of Pisa, Italy.
  • ArchettiF., BetroB. and SteffeS. (1975). A theoretical framework for global optimization via random sampling. Technical Report. University of Pisa, Italy.
  • ArchettiF. and BetroB. (1978). A priori analysis of deterministic strategies for global optimization In DixonL.C.W. and SzegöG.P. (Editors), Towards Global Optimization 2. North-Holland, Amsterdam.
  • BeckerR.W. and LagoG.V. (1970). A global optimization algorithm. In Proceedings of the 8th Allerton Conference on Circuits and System Theory.
  • BentleyJ.L., WeideB.W. and YaoA.C. (1980). Optimal expected-time algorithms for closest point problems. ACM Transactions on Mathematical Software, 6, 563–580.
  • BetroB. and De BiaseL. (1976). A recursive spline technique for uniform approximation of sampled data. Technical Report. University of Pisa, Italy.
  • BetroB. (1981). Bayesian testing of nonparametric hypothesis and its application to global optimization. Technical Report. IAMI, Italy.
  • BocharovN. and FeldbaumA.A. (1962). An automatic optimizer for the search of the smallest of several minima. Automatation and Remote Control, 23, no. 3.
  • BoenderC.G.E. and ZielinskiR. (1982). A sequential Bayesian approach to estimating the dimension of a multinomial distribution. Technical Report. The Institute of Mathematics of the Polish Academy of Sciences.
  • BoenderC.G.E., Rinnooy KanA.H.G., StougieL. and TimmerG.T. (1982). A stochastic method for global optimization. Mathematical Programming, 22, 125–140.
  • BoenderC.G.E. and Rinnooy KanA.H.G. (1983a). A Bayesian analysis of the number of cells of a multinomial distribution. The Statistician, 32.
  • BoenderC.G.E. and Rinnooy KanA.H.G. (1983b). Bayesian stopping rules for a class of stochastic global optimization methods. Technical report. Erasmus University Rotterdam, The Netherlands.
  • BraninF.H. and HooS.K. (1972). A method for finding multiple extrema of a function of n variables. In LootsmaF.A. (Editor). Numerical methods of nonlinear optimization. Academic Press, London.
  • BremmermanH. (1970). A method of unconstrained global optimization Mathematical Biosciences, 9, 1–15.
  • BrianJ.K. (1971). Classification and clustering using density estimation. Ph.D. Dissertation, University of Missouri.
  • BrooksS.H. (1958). A discussion of random methods for seeking maxima. Operations Research, 6, 244–251.
  • CacoullosT. (1966). Estimation of a multivariable density. Annals of the Institute of Statistics and Mathematics. 18, 179–189.
  • ChichinadzeV.K. (1967). Random search to determine the extremum of a function of several variables. Engineering Cybernetics, 1, 115–123.
  • De BlaseL. and FrontiniF. (1978). A stochastic method for global optimization; its structure and numerical performance. In DixonL.C.W. and SzegöG.P. (Editors). Towards Global Optimization 2, North–Holland, Amsterdam.
  • De HaanL. (1981). Estimation of the minimum of a function using order statistics. Journal of the American Statistical Association. 76, 467–469.
  • DevroyeL. (1978). Progressive global random search of continuous functions. Mathematical Programming. 15, 330–342.
  • DevroyeL. (1979). A bibliography on random search. Technical Report. SOCS, McGill Univ. Montreal.
  • DixonL.C.W. and SzegöG.P. (Editors) (1975). Towards Global Optimization. (North-Holland, Amsterdam).
  • DixonL.C.W., GomulkaJ. and SzegöG.P. (1975). Towards Global Optimization. In DixonL.C.W. and SzegöG.P. (Editors), Towards Global Optimization. North-Holland, Amsterdam.
  • DixonL.C.W. (1978). Global optima without convexity. Technical Report. Numerical Optimization Centre, Hatfield Polytechnic, England.
  • DixonL.C.W. and SzegöG.P. (Editors) (1978a). Towards Global Optimization 2. North-Holland, Amsterdam.
  • DixonL.C.W. and SzegöG.P. (1978b). The Global Optimization Problem. In DixonL.C.W. and SzegöG.P. (Editors), Towards Global Optimization 2. North-Holland, Amsterdam.
  • GavioniM. (1975). Necessary and sufficient conditions for the convergence of an algorithm in unconstrained minimization. In DixonL.C.W. and SzegöG.P. (Editors), Towards Global Optimization. North-Holland, Amsterdam.
  • GomulkaJ. (1978). Two implementations of Branin's method: Numerical experience. In DixonL.C.W. and Szegö (Editors), Towards Global Optimization 2. North-Holland, Amsterdam.
  • HartmanJ.K. (1973). Some experiments in global optimization. Naval Research Logistic Quarterly, 20, 569–576.
  • KemnaA.G.Z., Rinnooy KanA.H.G. and TimmerG.T. (1984). A stochastic method for constrained global optimization. Technical Report. Erasmus University Rotterdam, The Netherlands (to appear).
  • KushnerM.J. (1962). A versatile stochastic model of a function of unknown and time varying form. Journal of Mathematical Analysis and Applications, 5, 150–167.
  • KushnerM.J. (1964). A new method for locating the maximum point of an arbitrary multipeak curve in presence of noise. Journal of Basic Engineering, 97–106.
  • LawrenceJ.P. and SteiglitzK. (1972). Randomized pattern search. IEEE Transactions on Computers, c–21, 382–385.
  • LevyA. and GomezS (1980). The tunneling algorithm for the global optimization problem of constrained functions. Technical Report. Universidad Nacional Autonoma de Mexico.
  • MikhalskiiA.J. (1974). The method of average splines in the problem of approximating dependencies on the basis of empirical data. Automation and Remote Control, 35, 1–15.
  • MockusJ. (1975). On Bayesian methods of optimization. In DixonL.C.W. and SzegöG.P. (Editors), Towards Global Optimization. North-Holland, Amsterdam.
  • MockusJ., TiesisV. and ZilinskasA. (1978). The application of Bayesian methods for seeking the extremum. In DixonL.C.W. and SzegöG.P. (Editors), Towards Global Optimization 2. North-Holland, Amsterdam.
  • MoodA.M., GraybillF.A. and BoesD.C. (1974). Introduction to the theory of statistics. McGraw-Hill.
  • OuwensJ., Rinnooy KanA.H.G. and TimmerG.T. (1984). Multi level single linkage clustering in global optimization. Technical Report. Erasmus University Rotterdam, The Netherlands (to appear).
  • ParzenE. (1962). On estimation of a probability density function and mode. Annals of Mathematical Statistics, 33, 1065–1076.
  • PostmusJ., Rinnooy KanA.H.G. and TimmerG.T. (1983). An efficient dynamic selection method. Communications of the A.C.M., 26, 878–881.
  • PriceW.L. (1978). A controlled random search procedure for global optimization. In DixonL.C.W. and SzegöG.P. (Editors), Towards Global Optimization 2. North-Holland, Amsterdam.
  • Rinnooy KanA.H.G., RuygrokA. and TimmerG.T. (1984). Mode analysis in global optimization. Technical Report. Erasmus University Rotterdam, The Netherlands (to appear).
  • SchrachG. and ChoitM. (1976). Optimized relative step size random searches. Mathematical Programming, 10, 230–244.
  • SheppL.A. (1979). The joint density of the maximum and its location for a Wiener process with drift. Journal of Applied Probability, 16, 423–427.
  • SolisF.J. and WetsR.J.E. (1981). Minimizations by random search techniques. Mathematics of Operations Research, 6, 19–30.
  • SpircuL. (1979). Cluster analysis in global optimization. Economic Computation and Economic Cybernetic Studies and Research, 13, 43–50.
  • TreccaniG. (1975). On the convergence of Branin's method: a counter example. In DixonL.C.W. and SzegöG.P. (Editors), Towards Global Optimization. North-Holland, Amsterdam.
  • TörnA.A. (1976). Cluster analysis using seed points and density determined hyperspheres with an application to global optimization. In Proceedings of the third International conference on Pattern Recognition, Coronado, California.
  • TörnA.A. (1978). A search clustering approach to global optimization. In DixonL.C.W. and SzegöG.P. (Editors), Towards Global Optimization 2. North-Holland, Amsterdam.
  • ZielinskiR. (1981). A stochastic estimate of the structure of multi-extremal problems. Mathematical Programming, 21, 348–356.
  • ZilinskasA. (1982). Axiomatic approach to statistical models and their use in multimodal optimization theory. Mathematical Programming, 22, 104–116.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.