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Global optimization by multilevel coordinate search. (English) Zbl 0956.90045
The authors consider the bound constrained optimization problem \[ \text{Minimize \(f(x)\) subject to }u\leq x\leq v, \] with \(u,v\) being \(n\)-dimensional vectors with components in \(R\cup \{-\infty, \infty\}\). The algorithm described in this paper is an intermediate between purely heuristic methods and methods that allows an assessment of the quality of the minimum obtained. It is similar to the method for global optimization described by D. R. Jones, C. D. Perttunen and B. E. Stuckman [“Lipschitzian optimization without the Lipschitz constant”, J. Optim. Theory Appl. 79, 157-181 (1993; Zbl 0796.49032)].
As the latter method, the method suggested in this paper guarantees the convergence if the objective function is continuous in the neighborhood of the global minimizer and no other additional smoothness properties are required. Furthermore, the algorithm contains local enhacements, so that a quick convergence is ensured once the global part of the algorithm has found a point in the basic of attraction of a global minimizer. In the concluding part of the paper, some numerical results are presented.

90C30 Nonlinear programming
90C26 Nonconvex programming, global optimization
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