# Dual NUP Representations and Min-Maximization in Factor Graphs

arXiv: https://arxiv.org/abs/2501.12113 · HTML: https://mlsanity.com/paper/2501.12113/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 20 references that are in the map.
- First posted on arXiv 21 Jan 2025.

## Builds on (most cited first, 3 of 3)

- [Clarabel: An interior-point solver for conic programs with quadratic objectives](https://mlsanity.com/paper/2405.12762/) (2024)
- [Playing with Duality: An Overview of Recent Primal-Dual Approaches for Solving Large-Scale Optimization Problems](https://mlsanity.com/paper/1406.5429/) (2014)
- [Operator splitting for a homogeneous embedding of the linear complementarity problem](https://mlsanity.com/paper/2004.02177/) (2020)

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

- [L1 Regularization Paths in Linear Models by Parametric Gaussian Message Passing](https://mlsanity.com/paper/2604.16949/) (2026)

## Abstract (arXiv)

Normals with unknown parameters (NUP) can be used to convert nontrivial model-based estimation problems into iterations of linear least-squares or Gaussian estimation problems. In this paper, we extend this approach by augmenting factor graphs with convex-dual variables and pertinent NUP representations. In particular, in a state space setting, we propose a new iterative forward-backward algorithm that is dual to a recently proposed backward-forward algorithm.