Legendre-type integrands and convex integral functions

2012/08/26 by Jonathan M. Borwein, Borwein, Jonathan M., Liangjin Yao +1 · 1 citation
Mathematics · #34H05 #47N10 #90C25 #Advanced Banach Space Theory #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #Optimization and Control (math.OC) #Primary 46B20 #Secondary 47H05

paper · pdf · doi:10.48550/arxiv.1208.5217

openalex publication_date 2012/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the properties of integral functionals induced on L¹_E (S,μ) by closed convex functions on a Euclidean space E. We give sufficient conditions for such integral functions to be strongly rotund (well-posed). We show that in this generality functions such as the Boltzmann-Shannon entropy and the Fermi-Dirac entropy are strongly rotund. We also study convergence in measure and give various limiting counterexample.

Citations

• Generalized minimizers of convex integral functionals, Bregman distance, Pythagorean identities

Cited by

• Proximal Averages for Minimization of Entropy Functionals

Related

• On the Convexity of the Bernardi Integral Operator
• L^p-Legendre Transforms and Mahler integrals: Asymptotics and the Fokker--Planck heat flow
• Starlikeness and convexity of integral operators involving Mittag-Leffler functions
• Constrained Functional Value under General Convexity Conditions with Applications to Distributed Simulation
• The Legendre Transform in Modern Optimization