Global Optimization Using the Branch-And-Bound Algorithm with a Combination of Lipschitz Bounds over Simplices
Global Optimization Using the Branch-And-Bound Algorithm with a Combination of Lipschitz Bounds over Simplices

Summary/Abstract: Many problems in economy may be formulated as global optimization problems. Most numerically promising methods for solution of multivariate unconstrained Lipschitz optimization problems of dimension greater than 2 use rectangular or simplicial branch-and-bound techniques with computationally cheap, but rather crude lower bounds. The proposed branch-and-bound algorithm with simplicial partitions for global optimization uses a combination of 2 types of Lipschitz bounds. One is an improved Lipschitz bound with the first norm. The other is a combination of simple bounds with different norms. The efficiency of the proposed global optimization algorithm is evaluated experimentally and compared with the results of other well-known algorithms. The proposed algorithm often outperforms the comparable branch-and-bound algorithms.

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