论文标题
对于“直接搜索不连续函数的分析”的结果，拨言，反例和另一个揭示的民意测验步骤''
Erratum, counterexample and an additional revealing poll step for a result of "Analysis of direct searches for discontinuous functions''
论文作者
论文摘要
本说明提供了对本文“直接搜索不连续函数的分析”的最后一部分中宣布的定理的反例，数学编程卷。 133，pp。〜299--325，2012。反例涉及一个目标函数$ f：\ mathbb {r} \ to \ mathbb {r} $，它满足了定理所需的所有假设，但与其一些结论相矛盾。该定理的推论也受此反例的影响。反例显示的主要缺陷是，定向直接搜索方法（DDSM）可能会生成一系列试验点$（x_k）_k $收敛到点$ x _*$中的$ f $不连续且目标函数值$ f（x _*）$严格低于$ \ lim_ flim___________________ \ f（此外，DDSM在$ f $接近$ x _*$的两个分支之一中没有生成试验点。本说明还研究了定理的证明，以突出原始论文中的不精确陈述。最后，这项工作以DDSM的修改结束，允许恢复反例子破裂的属性。
This note provides a counterexample to a theorem announced in the last part of the paper ''Analysis of direct searches for discontinuous functions'', Mathematical Programming Vol. 133, pp.~299--325, 2012. The counterexample involves an objective function $f: \mathbb{R} \to \mathbb{R}$ which satisfies all the assumptions required by the theorem but contradicts some of its conclusions. A corollary of this theorem is also affected by this counterexample. The main flaw revealed by the counterexample is the possibility that a directional direct search method (dDSM) generates a sequence of trial points $(x_k)_k$ converging to a point $x_*$ where $f$ is discontinuous and whose objective function value $f(x_*)$ is strictly less than $\lim_{k\to\infty} f(x_k)$. Moreover the dDSM generates no trial point in one of the two branches of $f$ near $x_*$. This note also investigates the proof of the theorem to highlight the inexact statements in the original paper. Finally this work concludes with a modification of the dDSM that allows to recover the properties broken by the counterexample.
