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A new global optimization method for a symmetric Lipschitz continuous function and the application to searching for a globally optimal partition of a one-dimensional set. (English) Zbl 1377.65067
The paper proposes a method for solving a global optimization problem for a symmetric Lipschitz continuous function. The author shows that this problem always has a solution with natural conditions on the data. The proposed method is illustrated by solving a center-based clustering problem with synthetic data. Some numerical experiments are presented by testing the proposed method on the image segmentation problem.

65K05 Numerical mathematical programming methods
90C26 Nonconvex programming, global optimization
90C27 Combinatorial optimization
90C56 Derivative-free methods and methods using generalized derivatives
90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut
05E05 Symmetric functions and generalizations
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
Full Text: DOI
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