  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.
