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:arXiv.org
Main Authors: Zhou, Wei, Ali, M Montaz
Format: Paper
Language:English
Published: Ithaca Cornell University Library, arXiv.org 23.02.2015
Subjects:
Algorithms
Approximation
Mathematical analysis
Mixed integer
Nonlinear programming
ISSN:2331-8422
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.
Bibliography:SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
content type line 50
ISSN:2331-8422
DOI:10.48550/arxiv.1502.06315