On convex lower-level black-box constraints in bilevel optimization with an application to gas market models with chance constraints

Abstract Bilevel optimization is an increasingly important tool to model hierarchical decision making. However, the ability of modeling such settings makes bilevel problems hard solve in theory and practice. In this paper, we add on general difficulty class by further incorporating convex black-box constraints lower level. For setup, develop a cutting-plane algorithm that computes approximate bilevel-feasible points. We apply method European gas market which use joint chance constraint uncertain loads. Since not available closed form, fits into setting studied before. applied model, problem-specific insights derive bounds objective value problem. By doing so, are able show application problem global optimality. our numerical case study thus evaluate welfare sensitivity dependence achieved safety level load coverage.