# Differential properties of Euclidean projection onto power cone

In this paper, we study differential properties of Euclidean projection onto the power cone $K^{(p,q)}_n=\{(x,y,z)\in \mathbb{R}_+\times \mathbb{R}_+\times \mathbb{R}^n,\norm{z} \leq x^p y^q\}$, where $0< p,q < 1, p+q=1$. Projections onto certain power cones are examples of semismooth but non-strongly-semismooth projection onto a convex cone.

## Citation

Division of Mathematical Sciences, School of Physical & Mathematical Sciences, Nanyang Technological University, Singapore 637371.