# Projection: A Unified Approach to Semi-Infinite Linear Programs and Duality in Convex Programming

arXiv: https://arxiv.org/abs/1304.3030 · HTML: https://mlsanity.com/paper/1304.3030/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Apr 2013.

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

- [Vector Bellman Theory for Multichain Robust Average-Reward Markov Decision Processes](https://mlsanity.com/paper/2609.28792/) (2026)

## Abstract (arXiv)

Fourier-Motzkin elimination is a projection algorithm for solving finite linear programs. We extend Fourier-Motzkin elimination to semi-infinite linear programs which are linear programs with finitely many variables and infinitely many constraints. Applying projection leads to new characterizations of important properties for primal-dual pairs of semi-infinite programs such as zero duality gap, feasibility, boundedness, and solvability. Extending the Fourier-Motzkin elimination procedure to semi-infinite linear programs yields a new classification of variables that is used to determine the existence of duality gaps. In particular, the existence of what the authors term dirty variables can lead to duality gaps. Our approach has interesting applications in finite-dimensional convex optimization. For example, sufficient conditions for a zero duality gap, such as existence of a Slater point, are reduced to guaranteeing that there are no dirty variables. This leads to completely new proofs of such sufficient conditions for zero duality.