# On the Finite Number of Directional Stationary Values of Piecewise Programs

arXiv: https://arxiv.org/abs/1803.00190 · HTML: https://mlsanity.com/paper/1803.00190/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Mar 2018.

## Built on by (most cited first, 1 of 1)

- [Data-driven Piecewise Affine Decision Rules for Stochastic Programming with Covariate Information](https://mlsanity.com/paper/2304.13646/) (2023)

## Abstract (arXiv)

Extending a fundamental result for (indefinite) quadratic programs, this paper shows that certain non-convex piecewise programs have only a finite number of directional stationary values, and thus, possess only finitely many locally minimum values. We present various special cases of our main results, in particular, an application to a least-squares piecewise affine regression problem for which every directional stationary point is locally minimizing.