# A center-cut algorithm for solving convex mixed-integer nonlinear programming problems

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Abstract

In this paper, we present a new algorithm for solving convex mixed-integer nonlinear programming problems. Similarly to other linearization-based methods, the algorithm generates a polyhedral approximation of the feasible region. The main idea behind the algorithm is to use a different approach for obtaining trial solutions. Here trial solutions are chosen as a center of the polyhedral approximation. By choosing the trial solutions as such, the algorithm is more likely to obtain feasible solutions within only a few iterations, compared to the approach of choosing trial solutions as the minimizer of a linear approximation of the problem. The algorithm can be used both as a technique for finding the optimal solution or as a technique for quickly finding a feasible solution to a given problem. The algorithm has been applied to some challenging test problems, and for these the algorithm is able to find a feasible solution within only a few iterations.