# A mixed-integer approximation of robust optimization problems with mixed-integer adjustments

## TL;DR

This paper introduces a mixed-integer approximation method for complex adjustable-robust optimization problems with mixed variables, enabling more efficient solutions especially in power system applications.

## Contribution

It proposes a novel mixed-integer approximation technique for trilevel robust optimization problems with mixed variables, simplifying them into single-level problems.

## Key findings

- Allows exact or approximate representation of trilevel problems as mixed-integer problems.
- Enables use of efficient mixed-integer programming solvers.
- Demonstrates effectiveness in power system optimization, particularly smart converter control.

## Abstract

In the present article we propose a mixed-integer approximation of adjustable-robust optimization (ARO) problems, that have both, continuous and discrete variables on the lowest level. As these trilevel problems are notoriously hard to solve, we restrict ourselves to weakly-connected instances. Our approach allows us to approximate, and in some cases exactly represent, the trilevel problem as a single-level mixed-integer problem. This allows us to leverage the computational efficiency of state-of-the-art mixed-integer programming solvers. We demonstrate the value of this approach by applying it to the optimization of power systems, particularly to the control of smart converters.