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Linear decomposition approach for a class of nonconvex programming problems
Peiping Shen1,2, Chunfeng Wang1,2
1College of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007 P.R. China.
Abstract:
This paper presents a linear decomposition approach for a class of nonconvex programming problems by dividing the input space into polynomially many grids. It shows that under certain assumptions the original problem can be transformed and decomposed into a polynomial number of equivalent linear programming subproblems. Based on solving a series of liner programming subproblems corresponding to those grid points we can obtain the near-optimal solution of the original problem. Compared to existing results in the literature, the proposed algorithm does not require the assumptions of quasi-concavity and differentiability of the objective function, and it differs significantly giving an interesting approach to solving the problem with a reduced running time.
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