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A radial basis function method for global optimization. (English) Zbl 0972.90055
Global minimization problem is considered assuming the objective function be continuous and feasible region be a compact set of \(\mathbb{R}^d\). The objective function is supposed expensive. Therefore, computing intensive choice of the next trial point is justified involving optimization of an utility function. A radial function based interpolant of the objective function is constructed and used to define utility of the next trial point. The auxiliary problem of utility minimization is solved by means of a version of tunneling algorithm. The convergence of the proposed method is proved, and its relation to the statistically justified P-algorithm is analysed. Testing results for known test functions are presented.

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