In this paper, we design a Branch and Bound algorithm based on interval arithmetic to address nonconvex robust optimization problems. This algorithm provides the exact global solution of such difficult problems arising in many real life applications. A code was developed in MatLab and was used to solve some robust nonconvex problems with few variables. This first numerical study shows the interest of this approach providing the global solution of such difficult robust nonconvex optimization problems.

中文翻译：

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全局鲁棒优化的区间分支定界方法

在本文中，我们设计了一种基于区间算法的分支定界算法，以解决非凸鲁棒优化问题。该算法为许多现实应用中出现的此类难题提供了精确的全局解决方案。MatLab中开发了一个代码，用于解决一些变量很少的鲁棒非凸问题。首次数值研究表明，这种方法的兴趣在于为此类困难的鲁棒非凸优化问题提供全局解决方案。