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

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...

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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 181; no. 3; pp. 840 - 863
Main Authors: Wei, Zhou, Ali, M. Montaz, Xu, Liang, Zeng, Bo, Yao, Jen-Chih
Format: Journal Article
Language:English
Published: New York Springer US 01.06.2019
Springer Nature B.V
Subjects:
Algorithms
Applications of Mathematics
Approximation
Benders decomposition
Calculus of Variations and Optimal Control; Optimization
Decomposition
Engineering
Feasibility
Mathematical analysis
Mathematics
Mathematics and Statistics
Nonlinear programming
Operations Research/Decision Theory
Optimization
Theory of Computation
Subgradient
Generalized Benders decomposition
90C30
Mixed-integer nonlinear programming
90C25
90C11
Master program
Outer approximation
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Summary: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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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-019-01499-7