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Convex mixed integer nonlinear programming problems and an outer approximation algorithm. (English) Zbl 1327.90144
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.

90C11 Mixed integer programming
90C25 Convex programming
90C30 Nonlinear programming
Bonmin; AlphaECP; LaGO
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