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Convex mixed integer nonlinear programming problems and an outer approximation algorithm

Zhou Wei () and Majid Ali ()

Journal of Global Optimization, 2015, vol. 63, issue 2, 213-227

Abstract: 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. Copyright Springer Science+Business Media New York 2015

Keywords: Convex MINLP; Outer approximation; Decomposition; Master program; 90C11; 90C25; 90C30 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10898-015-0284-5

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