Obtaining guaranteed lower bounds for problems with unknown algebraic form has been a major challenge in derivative-free optimization. In this work, we present a deterministic global optimization method for black-box problems where the derivatives are not available or it is computationally expensive to obtain. However, a global upper bound on the diagonal Hessian elements is known. An edge-concave underestimator (Hasan in J Glob Optim 71:735–752, 2018) can be then constructed with vertex polyhedral solution. Evaluating this underestimator only at the vertices leads to a valid lower bound on the original black-box problem. We have implemented this lower bounding technique within a branch-and-bound framework and assessed its computational performance in locating \(\epsilon \)-global optimal solution for several box-constrained, nonconvex black-box functions.

中文翻译：

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有界Hessian的黑箱问题的确定性全局无导数优化

对于无代数形式的问题，获得有保证的下界一直是无导数优化的主要挑战。在这项工作中，我们为黑盒问题提供了确定性的全局优化方法，在这种情况下，导数不可用或获得的计算量很大。但是，已知对角线Hessian元素的全局上限。然后可以使用顶点多面体解构造边缘凹形低估量（Hasan，J Glob Optim 71：735–752，2018年）。仅在顶点处评估此低估器会导致原始黑盒问题的有效下限。我们已经在分支定界框架中实现了该下限技术，并在定位\（\ epsilon \）时评估了其计算性能。-几个盒约束，非凸黑盒函数的全局最佳解决方案。