2015/02/13 by Khanh Pham Duy, Duy, Khanh Pham, Marc Lassonde +1
Computer Science · Mathematics · #26B25 #52A41 #Analytic and geometric function theory #FOS: Mathematics #Nonlinear Differential Equations Analysis #Optimization and Control (math.OC) #Optimization and Variational Analysis
paper · pdf · doi:10.48550/arxiv.1502.03897
openalex publication_date 2015/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let E be a real vector space with dual space E^* and let C⊂ E be a convex subset with more than one point. Let f : C→ℝ be a function satisfying a mild stability property at 'flat' points of the (relative) boundary of C. We show that f is convex if and only if for some linear form c^* on E not constant on C, the function f+λc^* is quasiconvex for all λ∈ℝ.