标题： 具有低维子空间技术的可扩展无导数优化算法 显示英文标题

标题： Scalable Derivative-Free Optimization Algorithms with Low-Dimensional Subspace Techniques

摘要： 我们重新引入一个无导数子空间优化框架，该框架源自作者在Ya-xiang Yuan监督下的博士论文[Z. Zhang, 关于无导数优化方法，博士论文，中国科学院，北京，2012]第5章。在每次迭代中，该框架基于近似梯度定义一个（低维）子空间，然后在此子空间中求解一个子问题以生成一个新的迭代点。我们简要描述该框架的全局收敛性和最坏情况复杂性分析，详细说明其实施方法，并展示了一些数值结果，这些结果使用仅不精确的函数值解决了维度高达10^4的问题。 显示英文摘要

摘要： We re-introduce a derivative-free subspace optimization framework originating from Chapter 5 of the Ph.D. thesis [Z. Zhang, On Derivative-Free Optimization Methods, Ph.D. thesis, Chinese Academy of Sciences, Beijing, 2012] of the author under the supervision of Ya-xiang Yuan. At each iteration, the framework defines a (low-dimensional) subspace based on an approximate gradient, and then solves a subproblem in this subspace to generate a new iterate. We sketch the global convergence and worst-case complexity analysis of the framework, elaborate on its implementation, and present some numerical results on solving problems with dimensions as high as 10^4 using only inaccurate function values.