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A cut-peak function method for global optimization. (English) Zbl 1166.65030
Summary: A new method is proposed for solving box constrained global optimization problems. The basic idea of the method is described as follows: Constructing a so-called cut-peak function and a choice function for each present minimizer, the original problem of finding a global solution is converted into an auxiliary minimization problem of finding local minimizers of the choice function, whose objective function values are smaller than the previous ones. For a local minimum solution of auxiliary problems this procedure is repeated until no new minimizer with a smaller objective function value could be found for the last minimizer. Construction of auxiliary problems and choice of parameters are relatively simple, so the algorithm is relatively easy to implement, and the results of the numerical tests are satisfactory compared to other methods.

MSC:
65K05 Numerical mathematical programming methods
90C30 Nonlinear programming
90C59 Approximation methods and heuristics in mathematical programming
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