Minimization Problems on Strictly Convex Divergences

TL;DR

This paper investigates the properties of differentiable, strictly convex divergences, establishing conditions for minimizers, their uniqueness, and related geometric insights without relying on specific divergence forms.

Contribution

It provides general minimizer conditions and geometric properties for strictly convex divergences, extending understanding beyond particular divergence functions.

Findings

Minimizer conditions for strictly convex divergences

Uniqueness of minimizers without specific divergence forms

Geometric properties related to divergence minimization

Abstract

The divergence minimization problem plays an important role in various fields. In this note, we focus on differentiable and strictly convex divergences. For some minimization problems, we show the minimizer conditions and the uniqueness of the minimizer without assuming a specific form of divergences. Furthermore, we show geometric properties related to the minimization problems.