The recent paper (DOI: 10.1007/s10898-017-0537-6) suggests various practical tests (sufficient conditions) for checking pseudoconvexity of a twice differentiable function on an interval domain. The tests were implemented using interval extensions of the gradient and the Hessian of the function considered. In this paper, we present an alternative approach which is based on the use of more accurate affine form enclosures and affine arithmetic. We modify the tests to work with linear interval parametric enclosures of the gradients and the Hessians. We also present computational complexity results, showing that performing some tests exactly is NP-hard. It is shown by numerical experiments on random and benchmark data that the new approach results in more efficient tests for checking pseudoconvexity, however, at the expense of higher computation time.

最近的论文（DOI：10.1007 / s10898-017-0537-6）提出了各种实践测试（充分条件），用于检查区间域上二次可微函数的伪凸性。使用梯度的间隔扩展和所考虑函数的Hessian进行测试。在本文中，我们提出了一种替代方法，该方法基于使用更精确的仿射形式包围和仿射算法。我们修改测试以使用渐变和Hessians的线性间隔参数包围。我们还给出了计算复杂度的结果，表明准确地执行某些测试是NP难的。通过对随机数据和基准数据进行的数值实验表明，该新方法可以更有效地测试伪凸性，但是却要花费更多的计算时间。