# Some notes on continuity in convex optimization

**Authors:** Torbjørn Cunis  
**arXiv:** [2104.15045](https://arxiv.org/abs/2104.15045)  
**Date:** 2021-04-30  
**Summary page:** https://www.summarizepaper.com/fr/paper/2104.15045v1/

## Abstract

We provide proof that the optimal value function of a convex parametrized optimization problem in Euclidean spaces is itself a convex function onto the extended real line.