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

Zhou Wei (), M. Montaz Ali (), Liang Xu (), Bo Zeng () and Jen-Chih Yao ()
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Zhou Wei: Yunnan University
M. Montaz Ali: University of the Witwatersrand
Liang Xu: University of Pittsburgh
Bo Zeng: University of Pittsburgh
Jen-Chih Yao: Zhejiang Normal University

Journal of Optimization Theory and Applications, 2019, vol. 181, issue 3, No 8, 840-863

Abstract: 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.

Keywords: Mixed-integer nonlinear programming; Outer approximation; Generalized Benders decomposition; Subgradient; Master program; 90C11; 90C25; 90C30 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-019-01499-7

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