# Benson type algorithms for linear vector optimization and applications

arXiv: https://arxiv.org/abs/1302.2415 · HTML: https://mlsanity.com/paper/1302.2415/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Feb 2013.

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

- [γ-weakly θ-up-concavity: A Unified Framework for Non-Convex Optimization Beyond DR-Submodular and OSS Functions](https://mlsanity.com/paper/2602.13506/) (2026)

## Abstract (arXiv)

New versions and extensions of Benson's outer approximation algorithm for solving linear vector optimization problems are presented. Primal and dual variants are provided in which only one scalar linear program has to be solved in each iteration rather than two or three as in previous versions. Extensions are given to problems with arbitrary pointed solid polyhedral ordering cones. Numerical examples are provided, one of them involving a new set-valued risk measure for multivariate positions.