2020/03/24 by Eliahu Levy, Levy, Eliahu
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.2003.10941
openalex publication_date 2020/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this note we refine and improve some of the calculations in our 2019 article with Yair Censor (Applied Mathematics and Optimization, accepted for publication) where an analysis of the superiorization method is made via the principle of concentration of measure. Some paragraphs there are repeated here for the sake of completeness. Yet, for the case of accumulating 'steps' on the sphere, reference to distances as done there is replaced by reference to the angles, which makes simpler expressions. The treatment here of the action of a random transformation is also rather 'cleaner'. For some standard deviations, precise inequalities are here obtained rather then just O-expressions. Some further settings are mentioned, of no direct interest as per the latter article, showing results that similar calculations yield.