论文标题
经济不精确的恢复，用于最小化和应用
Economic inexact restoration for derivative-free expensive function minimization and applications
论文作者
论文摘要
事实证明，不精确的恢复方法是一种适当的工具，可以通过在目标函数中使用不同程度的精度来最大程度地限制任意可行设置中昂贵的功能的问题。不精确的恢复框架允许人们获得合理结合低精和高精度评估的方法的合适收敛性和复杂性结果。在本研究中，人们认识到许多具有昂贵目标功能的问题是非平滑的，有时甚至是不连续的。考虑到这一点，不精确的恢复方法扩展到了非平滑或不连续的情况。尽管在这种情况下不能使用依赖平滑度的优化阶段，但基本的收敛性和复杂性结果已恢复。定义了一个无衍生的优化阶段，并使用正则化方法来解决此阶段出现的子问题，该方法利用了不同的平稳性概念。新方法应用于复制模拟大坝故障的受控实验的问题。
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.
