Trade-off preservation in inverse multi-objective convex optimization

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.