In this paper, we present two new methods for solving convex mixed-integer nonlinear programming problems based on the outer approximation method. The first method is inspired by the level method and uses a regularization technique to reduce the step size when choosing new integer combinations. The second method combines ideas from both the level method and the sequential quadratic programming technique and uses a second order approximation of the Lagrangean when choosing the new integer combinations. The main idea behind the methods is to choose the integer combination more carefully at each iteration, in order to obtain the optimal solution in fewer iterations compared to the original outer approximation method. We prove rigorously that both methods will find and verify the optimal solution in a finite number of iterations. Furthermore, we present a numerical comparison of the methods based on 109 test problems to illustrate their advantages.

中文翻译：

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在凸 MINLP 的外逼近中使用正则化和二阶信息

在本文中，我们提出了两种基于外近似法求解凸混合整数非线性规划问题的新方法。第一种方法受到级别方法的启发，并在选择新的整数组合时使用正则化技术来减小步长。第二种方法结合了水平方法和顺序二次规划技术的思想，并在选择新的整数组合时使用拉格朗日的二阶近似。这些方法背后的主要思想是在每次迭代时更仔细地选择整数组合，以便与原始外逼近方法相比，在更少的迭代中获得最优解。我们严格证明这两种方法都会在有限的迭代次数中找到并验证最优解。此外，