# Tractability of Convex Vector Optimization Problems in the Sense of Polyhedral Approximations

## TL;DR

This paper investigates the conditions under which convex vector optimization problems can be approximated by polyhedral inner and outer bounds to their Pareto frontiers, revealing limitations and characterizations of tractability.

## Contribution

It provides a characterization of when CVOPs are tractable for polyhedral approximations based on weighted sum scalarization problems.

## Key findings

- Not all CVOPs are tractable for polyhedral approximations.
- Tractability is characterized by properties of weighted sum scalarizations.
- The study extends understanding of approximation limits in non-compact feasible regions.

## Abstract

There are different solution concepts for convex vector optimization problems (CVOPs) and a recent one, which is motivated from a set optimization point of view, consists of finitely many efficient solutions that generate polyhedral inner and outer approximations to the Pareto frontier. A CVOP with compact feasible region is known to be bounded and there exists a solution of this sense to it. However, it is not known if it is possible to generate polyhedral inner and outer approximations to the Pareto frontier of a CVOP if the feasible region is not compact. This study shows that not all CVOPs are tractable in that sense and gives a characterization of tractable problems in terms of the well known weighted sum scalarization problems.