2020/03/19 by Kananart Kuwaranancharoen, Kuwaranancharoen, Kananart, Shreyas Sundaram +1
Computer Science · Engineering · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Machine Learning and Algorithms #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques #math.OC
paper · pdf · doi:10.48550/arxiv.2003.09035
8 pages, 8 figures. To appear in the Proceedings of the 2020 American Control Conference, 1-3 July 2020, Denver, CO, USA
arxiv created 2020/03/19 · openalex publication_date 2020/03/19 · arxiv updated 2020/03/23 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
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.