Convergence rates of a global optimization algorithm Authors Regina Hunter Mladineo Rider College School of Business Administration Article

Received: 05 June 1987 Revised: 02 February 1990 DOI :
10.1007/BF01586051

Cite this article as: Mladineo, R.H. Mathematical Programming (1992) 54: 223. doi:10.1007/BF01586051
Abstract This paper presents a best and worst case analysis of convergence rates for a deterministic global optimization algorithm. Superlinear convergence is proved for Lipschitz functions which are convex in the direction of the global maximum (concave in the direction of the global minimum). Computer results are given, which confirm the theoretical convergence rates.

Key words Global optimization Lipschitz functions Download to read the full article text

References [1]

L.C.W. Dixon and G.P. Szego,Towards Global Optimisation 2 (North-Holland, Amsterdam, 1978).

[2]

Y.P. Evtushenko, “Numerical methods for finding global extrema of a non-uniform mesh,”USSR Computational Mathematics and Mathematical Physics 11 (1971).

[3]

P. Gill, W. Murray and M. Wright,Practical Optimization (Academic Press, London, 1981).

[4]

R. Horst, “A general class of branch-and-bound methods in global optimization,”Journal of Optimization Theory and Applications (1985).

[5]

R.H. Mladineo, “An algorithm for finding the global maximum of a multimodal, multivariate function,”Mathematical Programming 34 (1986) 188–200.

[6]

S.A. Pijavskii, “An algorithm for finding the absolute extremum of a function,”USSR Computational Mathematics and Mathematical Physics (1972) 57–67.

[7]

J. Pinter, “Globally convergent methods forn -dimensional multi-extremal optimization,”Optimisation 17 (1986).

[8]

H. Ratschek, “Inclusion functions and global optimization,”Mathematical Programming 33 (1985) 300–317.

[9]

B. Shubert, “A sequential method seeking the global maximum of a function,”SIAM Journal of Numerical Analysis 9(3) (1972) 379–388.

[10]

A.G. Sukharev, “A stochastic algorithm for extremum search, optimal in one step,”USSR Computational Mathematics and Mathematical Physics (1981) 23–39.

[11]

G.R. Wood, “Multidimensional bisection applied to global optimization,”Computers & Mathematics with Applications 21 (1991) 161–172.

© The Mathematical Programming Society, Inc. 1992