Set-Valued Analysis of Generalized Barycentric Coordinates and Their Geometric Properties

2023/05/05 by Fabio V. Difonzo, Difonzo, Fabio V.
Computer Science · Mathematics · #Optimization and Variational Analysis #Advanced Optimization Algorithms Research #Functional Equations Stability Results

paper · pdf · doi:10.48550/arxiv.2306.00710

Abstract

Letting P be a convex polytope in ℝ^d with n>d vertices, we study geometric and analytical properties of the set of generalized barycentric coordinates relative to any point p∈ P. We prove that such sets are polytopes in ℝⁿ with at most n-d-1 vertices, and provide results about continuity and differentiability for the corresponding set-valued maps.

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