# Trade-off preservation in inverse multi-objective convex optimization

## TL;DR

This paper introduces a novel inverse optimization approach for multi-objective convex problems that preserves decision maker's trade-offs, even with non-Pareto optimal inputs, and demonstrates its effectiveness on clinical prostate cancer data.

## Contribution

It develops a new inverse optimization method that accounts for non-Pareto solutions and preserves trade-offs, extending existing models with a linear approximation and efficient algorithm.

## Key findings

- Successfully applied to prostate cancer radiation therapy data
- Balances trade-off preservation with computational efficiency
- Encompasses many existing inverse models in the literature

## Abstract

We present a new inverse optimization methodology for multi-objective convex optimization that accommodates an input solution that may not be Pareto optimal and determines a weight vector that produces a Pareto optimal solution that approximates the input solution and preserves the decision maker's intention encoded in it. We introduce a notion of trade-off preservation, which we use as a measure of similarity for approximating the input solution, and show its connection with minimizing an optimality gap. Our inverse model maintains the complexity of the traditional inverse convex models. We propose a linear approximation to the model and a successive linear programming algorithm that balance between trade-off preservation and computational efficiency, and show that our model encompasses many of the existing models from the literature. We demonstrate the proposed method using clinical data from prostate cancer radiation therapy.