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Abstract
In this article, we discuss a class of continuous-time linear programming (CLP) problems. We provide a discrete approximation procedure to find numerical solutions of CLP, establish the estimation for the error bound and prove that the searched sequence of approximate solution functions weakly star converges to an optimal solution of CLP. Finally, we provide some numerical examples to implement our proposed method and to show the quality of the proposed error bound.
Acknowledgements
We thank the referees for providing the valuable comments which has definitely improved the presentation of this article. A special thanks also goes to Prof. Hsien-Chung Wu who helped us to thoroughly check the original manuscript and suggests the weak convergence to approximate the optimal solutions in the revision stage. This research is partially supported by NSC 99-2115-M-037-001, NSC 99-2115-M-238-001 and NSC 99-2115-M-033-005.