# On the spherical convexity of quadratic functions

## TL;DR

This paper investigates the conditions under which quadratic functions are spherically convex on specific convex sets related to positive orthants and Lorentz cones, enhancing understanding of spherical convexity in these contexts.

## Contribution

It provides new characterizations of spherical convexity for quadratic functions on sets associated with positive orthants and Lorentz cones.

## Key findings

- Conditions for spherical convexity on positive orthants
- Conditions for spherical convexity on Lorentz cones
- Characterizations applicable to quadratic functions in these settings

## Abstract

In this paper we study the spherical convexity of quadratic functions on spherically convex sets. In particular, conditions characterizing the spherical convexity of quadratic functions on spherical convex sets associated to the positive orthants and Lorentz cones are given.