Generating polyhedral outer approximations and solving mixed-integer linear relaxations remains one of the main approaches for solving convex mixed-integer nonlinear programming (MINLP) problems. There are several algorithms based on this concept, and the efficiency is greatly affected by the tightness of the outer approximation. In this paper, we present a new framework for strengthening cutting planes of nonlinear convex constraints, to obtain tighter outer approximations. The strengthened cuts can give a tighter continuous relaxation and an overall tighter representation of the nonlinear constraints. The cuts are strengthened by analyzing disjunctive structures in the MINLP problem, and we present two types of strengthened cuts. The first type of cut is obtained by reducing the right-hand side value of the original cut, such that it forms the tightest generally valid inequality for a chosen disjunction. The second type of cut effectively uses individual right-hand side values for each term of the disjunction. We prove that both types of cuts are valid and that the second type of cut can dominate both the first type and the original cut. We use the cut strengthening in conjunction with the extended supporting hyperplane algorithm, and numerical results show that the strengthening can significantly reduce both the number of iterations and the time needed to solve convex MINLP problems.

产生多面体外部逼近和求解混合整数线性松弛仍然是解决凸混合整数非线性规划（MINLP）问题的主要方法之一。有许多基于此概念的算法，效率受到外部近似紧密度的很大影响。在本文中，我们提出了一个新的框架，用于加强非线性凸约束的切割平面，以获得更紧密的外部近似。增强的切口可以提供更紧密的连续松弛，并且可以更严格地表示非线性约束。通过分析MINLP问题中的析取结构来增强切入点，我们介绍了两种类型的增强切入点。第一种类型的裁切是通过减少原始裁切的右侧值获得的，这样就形成了针对所选析取关系的最严格的一般有效不等式。第二种类型的切分有效地为每个析取项使用了单独的右侧值。我们证明两种类型的切割都是有效的，第二种切割可以同时控制第一种和原始切割。我们将割增强与扩展支持超平面算法结合使用，数值结果表明，该增强可以显着减少迭代次数和解决凸MINLP问题所需的时间。我们证明两种类型的切割都是有效的，并且第二种切割可以同时控制第一种和原始切割。我们将割增强与扩展支持超平面算法结合使用，数值结果表明，该增强可以显着减少迭代次数和解决凸MINLP问题所需的时间。我们证明两种类型的切割都是有效的，第二种切割可以同时控制第一种和原始切割。我们将割增强与扩展支持超平面算法结合使用，数值结果表明，该增强可以显着减少迭代次数和解决凸MINLP问题所需的时间。