# Some Black-box Reductions for Objective-robust Discrete Optimization Problems Based on their LP-Relaxations

## TL;DR

This paper introduces black-box reduction techniques that leverage LP-relaxations and integrality gap verifiers to develop approximation algorithms for robust discrete optimization problems under convex uncertainty sets.

## Contribution

It presents a novel method to transform non-robust LP relaxations into approximation algorithms for robust problems using integrality gap verifiers.

## Key findings

- Provides a framework for robust optimization using LP relaxations
- Demonstrates how to derive approximation algorithms for robust problems
- Connects integrality gap verifiers with robust optimization solutions

## Abstract

We consider robust discrete minimization problems where uncertainty is defined by a convex set in the objective. We show how an integrality gap verifier for the linear programming relaxation of the non-robust version of the problem can be used to derive approximation algorithms for the robust version.