Discrete and Continuous Bang-Bang and Facial Spaces Or: Look for the Extreme Points

1980/04/01 by Zvi Artstein · 2 citations
Computer Science · Mathematics · #Applied mathematics #Computer science #Functional Equations Stability Results #Fuzzy Systems and Optimization #Generalization #Hang #Lemma (botany) #Mathematical analysis #Mathematics #Norm (philosophy) #Optimization and Variational Analysis #Pure mathematics #Simple (philosophy)

paper · doi:10.1137/1022026

openalex publication_date 1980/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/04/04

Abstract

A simple geometrical argument is used to establish seemingly different continuous and discrete hang-hang type results. Among other applications we discuss the bang-bang principle for linear continuous control systems, a generalization to discrete systems, the ranges of vector integrals, the Shapley–Folkman lemma and the Carathéodory theorem, a moment problem, and a minimum norm problem.

Citations

• Elimination of Randomization in Certain Statistical Decision Procedures and Zero-Sum Two-Person Games
• How to Cut a Cake Fairly

Cited by

• Extreme point [wikipedia]
• Vector measure [wikipedia]