The paper defines the ambiguity premium Δ_ε(x) as the gap between pessimistic and optimistic upper-level values over ε-optimal follower responses and provides bounds plus a screening workflow to trace robustness-efficiency frontiers in bilevel problems.
Introduction to Mathematical Programming with Equilibrium Constraints (MPECs) and Bilevel Optimization
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abstract
Our aim is to explain mathematical programs with equilibrium constraints (MPECs), motivate them through applications, present the main equivalent formulations of equilibrium constraints, and summarize the basic existence theory for optimal solutions. The central message is that an MPEC is an optimization problem whose feasible set is partly defined by another optimization, variational inequality, complementarity system, or equilibrium model.
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math.OC 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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A Diagnostic Framework for Implementation Risk in Bilevel Decision Problems: The Ambiguity Premium and the Robustness--Efficiency Frontier
The paper defines the ambiguity premium Δ_ε(x) as the gap between pessimistic and optimistic upper-level values over ε-optimal follower responses and provides bounds plus a screening workflow to trace robustness-efficiency frontiers in bilevel problems.