We study the problem of finding the global optimum of a nonlinear real function over an interval box by means of complete search techniques, namely interval branch-and-bound algorithms. Such an algorithm typically generates a tree of boxes from the initial box by alternating branching steps and contraction steps in order to remove non optimal sub-boxes. In this paper, we introduce a new contraction method that is designed to handle the boundary of the initial box where a minimizer may not be a stationary point. This method exploits the first-order optimality conditions and we show that it subsumes the classical monotonicity test based on interval arithmetic. A new branch-and-bound algorithm has been implemented in the interval solver Realpaver. An extensive experimental study based on a set of standard benchmarks is presented.

中文翻译：

---

基于有界约束全局优化的最优条件的区间测试和承包商

我们研究了通过完全搜索技术，即区间分支定界算法，在区间框上寻找非线性实函数的全局最优值的问题。这种算法通常通过交替分支步骤和收缩步骤从初始框生成框树，以删除非最优子框。在本文中，我们介绍了一种新的收缩方法，该方法旨在处理最小化器可能不是静止点的初始框的边界。该方法利用一阶最优性条件，我们表明它包含了基于区间算术的经典单调性检验。在区间求解器 Realpaver 中实现了一种新的分支定界算法。提出了基于一组标准基准的广泛实验研究。