Convex mixed integer nonlinear programming problems and an outer approximation algorithm

In this paper, we mainly study one class of convex mixed-integer nonlinear programming problems (MINLPs) with non-differentiable data. By dropping the differentiability assumption, we substitute gradients with subgradients obtained from KKT conditions, and use the outer approximation method to refor...

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Bibliographic Details
Published in:Journal of global optimization Vol. 63; no. 2; pp. 213 - 227
Main Authors: Wei, Zhou, Ali, M. Montaz
Format: Journal Article
Language:English
Published: New York Springer US 01.10.2015
Springer
Springer Nature B.V
Subjects:
Algorithms
Applied mathematics
Approximation
Computer Science
Convergence
Convex analysis
Equivalence
Integer programming
Mathematical analysis
Mathematics
Mathematics and Statistics
Mixed integer
Nonlinear programming
Operations Research/Decision Theory
Optimization
Optimization algorithms
Real Functions
Variables
Convex MINLP
90C30
90C25
90C11
Master program
Decomposition
Outer approximation
ISSN:0925-5001, 1573-2916
Online Access:Get full text
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Summary:In this paper, we mainly study one class of convex mixed-integer nonlinear programming problems (MINLPs) with non-differentiable data. By dropping the differentiability assumption, we substitute gradients with subgradients obtained from KKT conditions, and use the outer approximation method to reformulate convex MINLP as one equivalent MILP master program. By solving a finite sequence of subproblems and relaxed MILP problems, we establish an outer approximation algorithm to find the optimal solution of this convex MINLP. The convergence of this algorithm is also presented. The work of this paper generalizes and extends the outer approximation method in the sense of dealing with convex MINLPs from differentiable case to non-differentiable one.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-015-0284-5