Abstract

Concave programming problems constitute one of the most important and fundamental classes of problems in global optimization. Concave minimization problems have a diverse range of direct and indirect applications. Moreover, concave minimization problems are well known to be NP-hard. In this paper, we present three algorithms which are similar to each other for concave minimization problems. In each iteration of the algorithms, linear programming problems with the same constraints as the initial problem are required to solve and a local search method is required to use. Furthermore, the convergence result is given. From the result, we see that the local search method is not necessarily required but we require that some conditions must hold on the constraint.

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