First order dependence on uncertainty sets in robust optimization

TL;DR

This paper demonstrates that a first order approximation can effectively estimate solutions to robust optimization problems when the uncertainty set is scaled, providing insights into the properties of this approximation.

Contribution

It introduces a first order approach to approximate robust optimization solutions and explores its properties, offering a new perspective on handling uncertainty sets.

Findings

First order approximation closely estimates robust solutions under scaled uncertainty.

The paper characterizes properties of the first order approximation.

Provides theoretical insights into the behavior of robust optimization with scaled uncertainty.

Abstract

We show that a first order problem can approximate solutions of a robust optimization problem when the uncertainty set is scaled, and explore further properties of this first order problem.