On contextual inverse multiobjective problems

• Inverse optimization framework with multiple criteria shaped by context features. • Decisions modeled via ideal point scalarization using norm-based distance metrics. • Characterizes inverse feasibility conditions using tools from convex analysis. • Structured sparsity constraints enhance interpretability of the inferred problem. • Validated on financial data, showing strong generalization and sparse recovery. We introduce a novel framework for Contextual Inverse Multiobjective Optimization, where the goal is to recover multiple objective functions and the preferences among them from observed context-decision pairs. Assuming that each decision arises from minimizing a weighted distance to an ideal outcome, we develop a mathematical programming model that infers context-dependent linear objectives consistent with observed data. Our approach accommodates different norm-based scalarizations, including ℓ 1 , ℓ 2 , ℓ ∞ and Ordered Weighted Averages, and enforces interpretability through structured sparsity. By characterizing the conditions under which observed decisions are provably optimal, we formulate a tractable Mixed-Integer Quadratic Program that reveals how contextual features influence decision-making criteria. Numerical experiments on real-world data demonstrate the method’s ability to recover interpretable, sparse models while maintaining strong generalization performance.