Stochastic global optimization methods part I: Clustering methods

In this stochastic approach to global optimization, clustering techniques are applied to identify local minima of a real valued objective function that are potentially global. Three different methods of this type are described; their accuracy and efficiency are analyzed in detail.

[1]  Kai Lai Chung,et al.  A Course in Probability Theory , 1949 .

[2]  Samuel H. Brooks.  A Discussion of Random Methods for Seeking Maxima , 1958 .

[3]  E. Parzen.  On Estimation of a Probability Density Function and Mode , 1962 .

[4]  R. R. Bahadur.  A Note on Quantiles in Large Samples , 1966 .

[5]  P. Wolfe.  Convergence Conditions for Ascent Methods. II , 1969 .

[6]  P. Wolfe.  Convergence Conditions for Ascent Methods. II: Some Corrections , 1971 .

[7]  Victor V. Ivanov.  Optimal Algorithms of Minimization in the Class of Functions with the Lipschitz Condition , 1971, IFIP Congress.

[8]  A. G. Sukharev.  Optimal strategies of the search for an extremum , 1971 .

[9]  J. K. Hartman.  Some experiments in global optimization , 1973 .

[10]  J. Spencer.  Probabilistic Methods in Combinatorics , 1974 .

[11]  P. Bloomfield,et al.  Properties of the random search in global optimization , 1975 .

[12]  Luc Devroye,et al.  Progressive global random search of continuous functions , 1978, Math. Program..

[13]  H. Zimmermann.  Towards global optimization 2: L.C.W. DIXON and G.P. SZEGÖ (eds.) North-Holland, Amsterdam, 1978, viii + 364 pages, US $ 44.50, Dfl. 100,-. , 1979 .

[14]  Leen Stougie,et al.  Global optimization : a stochastic approach , 1980 .

[15]  Reuven Y. Rubinstein,et al.  Simulation and the Monte Carlo method , 1981, Wiley series in probability and mathematical statistics.

[16]  Ryszard Zielinski.  A statistical estimate of the structure of multi-extremal problems , 1981, Math. Program..

[17]  Roger J.-B. Wets,et al.  Minimization by Random Search Techniques , 1981, Math. Oper. Res..

[18]  Alexander H. G. Rinnooy Kan,et al.  A stochastic method for global optimization , 1982, Math. Program..

[19]  B. Betrò.  Bayesian testing of nonparametric hypotheses and its application to global optimization , 1984 .

[20]  Cornelis Gustaaf Eduard Boender,et al.  The generalized multinomial distribution : a Bayesian analysis and applications , 1984 .

[21]  Alexander H. G. Rinnooy Kan,et al.  Stochastic methods for global optimization , 1984 .

[22]  G. T. Timmer,et al.  Stochastic global optimization methods part II: Multi level methods , 1987, Math. Program..

[23]  J. Snyman,et al.  A multi-start global minimization algorithm with dynamic search trajectories , 1987 .