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On Solving Nonsmooth Mixed-Integer Nonlinear Programming Problems by Outer Approximation and Generalized Benders Decomposition

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Abstract

In this paper, we mainly study nonsmooth mixed-integer nonlinear programming problems and solution algorithms by outer approximation and generalized Benders decomposition. Outer approximation and generalized Benders algorithms are provided to solve these problems with nonsmooth convex functions and with conic constraint, respectively. We illustrate these two algorithms by providing detailed procedure of solving several examples. The numerical examples show that outer approximation and generalized Benders decomposition provide a feasible alternative for solving such problems without differentiability.

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Acknowledgements

This research of the first author was supported by the National Natural Science Foundations of China (Nos. 11826204, 11826206 and 11771384), the Natural Science Foundation of Yunnan Province of China (No. 2018FB004) and the Scientific Research Foundation of Yunnan University under grant No. 2018YDJQ010, and by Joint Key Project of Yunnan Provincial Science and Technology Department and Yunnan University (No. 2018FY001(-014)) and IRTSTYN. The research work of Bo Zeng was supported by National Science Foundation CMMI-1436452. The research work of M. Montaz Ali was supported by the funding from NRF of South Africa (No. 114846). The research work of Jen-Chih Yao was partially supported by the Grant MOST 105-2221-E-039-009-MY3.

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Wei, Z., Ali, M.M., Xu, L. et al. On Solving Nonsmooth Mixed-Integer Nonlinear Programming Problems by Outer Approximation and Generalized Benders Decomposition. J Optim Theory Appl 181, 840–863 (2019). https://doi.org/10.1007/s10957-019-01499-7

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