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Vietnam Journal of Mathematics 35:4(2007) 463-479

 A Simplicial Algorithm for Concave Minimization and Its Performance as a Heuristic Tool

Takahito Kuno and Yoshiyuki Shiguro

Abstract.  In this paper, we develop a kind of branch-and-bound algorithm for solving concave minimization problems. We show that the algorithm converges to an optimal solution of this multiextremal global optimization problem, and that it generates a high-quality heuristic solution even if it is forced to terminate. Therefore, the algorithm can be used in two ways, as an exact algorithm and as a heuristic tool. We also report some numerical results of a comparison with an existing algorithm, and show the performance as a heuristic tool.

 

 

Keywords: Global optimization, concave minimization, branch-and-bound algorithm, simplicial algorithm, heuristic algorithm.

 

 

 

 

 

 

 

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