论文标题
在一组已知和未知函数总和的可能最小化中
On the Set of Possible Minimizers of a Sum of Known and Unknown Functions
论文作者
论文摘要
找到凸函数之和最小化的最小化器的问题对于优化领域至关重要。因此，了解该最小化器与总和中各个函数的属性有何关系。在本文中，我们考虑了总和中单个函数之一的情况。取而代之的是，只有一个包含未知函数的最小化器的区域以及一些一般特征（例如强凸参数）。考虑到有关整体功能一部分的有限信息，我们提供了必要的条件，该条件可用于在包含已知和未知功能之和最小化的区域上构造上限。在两种情况下，我们都提供了这种必要的条件，即未知函数最小化器的不确定性区域是任意的，并且在不确定性区域为球的具体情况下。
The problem of finding the minimizer of a sum of convex functions is central to the field of optimization. Thus, it is of interest to understand how that minimizer is related to the properties of the individual functions in the sum. In this paper, we consider the scenario where one of the individual functions in the sum is not known completely. Instead, only a region containing the minimizer of the unknown function is known, along with some general characteristics (such as strong convexity parameters). Given this limited information about a portion of the overall function, we provide a necessary condition which can be used to construct an upper bound on the region containing the minimizer of the sum of known and unknown functions. We provide this necessary condition in both the general case where the uncertainty region of the minimizer of the unknown function is arbitrary, and in the specific case where the uncertainty region is a ball.
