# On the spherical quasi-convexity of quadratic functions on spherical self-dual convex sets

## TL;DR

This paper investigates the conditions under which quadratic functions exhibit spherical quasi-convexity on specific convex sets, providing theoretical insights and characterizations relevant to optimization on spherical domains.

## Contribution

It offers new sufficient conditions and partial characterizations for spherical quasi-convexity of quadratic functions on spherically subdual convex sets.

## Key findings

- Sufficient conditions for spherical quasi-convexity are established.
- Partial characterization of quasi-convexity on spherical Lorentz sets is provided.
- Examples illustrating the theoretical results are included.

## Abstract

In this paper, the spherical quasi-convexity of quadratic functions on spherically subdual convex sets is studied. Sufficient conditions for spherical quasi-convexity on spherically subdual convex sets are presented. A partial characterization of spherical quasi-convexity on spherical Lorentz sets is given and some examples are provided.