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A new filled function method for unconstrained global optimization. (English) Zbl 1162.65033

The problem of finding a global minimum of a given function \(f(x)\) on \(\mathbb{R}^n\) is considered. It is assumed that \(f\) is Lipschitz continuous on \(\mathbb{R}^n\) and that \(f(x)\to\infty\) as \(\|x\|\to\infty\). This last assumption implies that there exists a compact set \(\Omega\subset \mathbb{R}^n\), the interior of which contains all minimizers of \(f(x)\), so that the original problem is equivalent to minimization of \(f(x)\) subject to \(x\in\Omega\). The authors propose a new filled function with two parameters (definition of the filled function see in [Y. J. Yang and Y. L. Shang, A new filled function method for constraint global optimization, Appl. Math. Comput. 173, 501–512 (2006; Zbl 1094.65063)] and develop a new algorithm for global minimization of \(f(x)\) using the proposed filled function. Theoretical and numerical properties of the proposed filled function are investigated. Satisfactory numerical properties of the algorithm are demonstrated on 7 test problems in the concluding part of the paper.

MSC:

65K05 Numerical mathematical programming methods
90C26 Nonconvex programming, global optimization

Citations:

Zbl 1094.65063
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References:

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