# Primal and Dual Approximation Algorithms for Convex Vector Optimization Problems

arXiv: https://arxiv.org/abs/1308.6809 · HTML: https://mlsanity.com/paper/1308.6809/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Aug 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)

Two approximation algorithms for solving convex vector optimization problems (CVOPs) are provided. Both algorithms solve the CVOP and its geometric dual problem simultaneously. The first algorithm is an extension of Benson's outer approximation algorithm, and the second one is a dual variant of it. Both algorithms provide an inner as well as an outer approximation of the (upper and lower) images. Only one scalar convex program has to be solved in each iteration. We allow objective and constraint functions that are not necessarily differentiable, allow solid pointed polyhedral ordering cones, and relate the approximations to an appropriate ε-solution concept. Numerical examples are provided.