用于无导数昂贵函数最小化的经济型非精确恢复及其应用
Economic inexact restoration for derivative-free expensive function minimization and applications
AI总结：
本文将 Inexact Restoration 扩展到非光滑或不连续的昂贵目标函数最小化，结合无导数优化与正则化子问题求解，保留收敛和复杂度保证，并用于模拟大坝失效实验。
摘要：
非精确恢复（Inexact Restoration）方法已被证明是处理以下问题的合适工具：在任意可行集内最小化昂贵函数，并在目标函数中采用不同精度。Inexact Restoration 框架能够为一种理性结合低精度与高精度评估的方法获得适当的收敛性和复杂度结果。在本研究中，人们认识到许多具有昂贵目标函数的问题是非光滑的，有时甚至是不连续的。基于此，Inexact Restoration 方法被扩展到非光滑或不连续情形。尽管依赖光滑性的优化阶段在此情形下无法使用，但基本的收敛性和复杂度结果仍得以恢复。文中定义了一个无导数优化阶段，并利用一种正则化方法求解该阶段产生的子问题，该方法利用了不同的平稳性概念。新方法被应用于复现一个模拟大坝失效的受控实验问题。
英文摘要：
The Inexact Restoration approach has proved to be an adequate tool for handling the problem of minimizing an expensive function within an arbitrary feasible set by using different degrees of precision in the objective function. The Inexact Restoration framework allows one to obtain suitable convergence and complexity results for an approach that rationally combines low- and high-precision evaluations. In the present research, it is recognized that many problems with expensive objective functions are nonsmooth and, sometimes, even discontinuous. Having this in mind, the Inexact Restoration approach is extended to the nonsmooth or discontinuous case. Although optimization phases that rely on smoothness cannot be used in this case, basic convergence and complexity results are recovered. A derivative-free optimization phase is defined and the subproblems that arise at this phase are solved using a regularization approach that take advantage of different notions of stationarity. The new methodology is applied to the problem of reproducing a controlled experiment that mimics the failure of a dam.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
