# Variational Analysis of the Ky Fan k-norm

arXiv: https://arxiv.org/abs/1601.07430 · HTML: https://mlsanity.com/paper/1601.07430/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jan 2016.

## Built on by (most cited first, 2 of 2)

- [A dual semismooth Newton based augmented Lagrangian method for large-scale linearly constrained sparse group square-root Lasso problems](https://mlsanity.com/paper/2111.13878/) (2021)
- [Fast Computation of Superquantile-Constrained Optimization Through Implicit Scenario Reduction](https://mlsanity.com/paper/2405.07965/) (2024)

## Abstract (arXiv)

In this paper, we will study some variational properties of the Ky Fan k-norm θ=|·|(k) of matrices, which are closed related to a class of basic nonlinear optimization problems involving the Ky Fan k-norm. In particular, for the basic nonlinear optimization problems, we will introduce the concept of nondegeneracy, strict complementarity and the critical cones associated with the generalized equations. Finally, we present the explicit formulas of the conjugate function of the parabolic second order directional derivative of θ, which will be referred to as the sigma term of the second order optimality conditions. The results obtain in this paper provide the necessary theoretical foundations for future work on sensitivity and stability analysis of the nonlinear optimization problems involving the Ky Fan k-norm.