Reformulating Bilevel Problems by SQP Embedding

Due to their inherently complex structure, bilevel optimization problems are often transformed into single‐level problems in order to make them numerically solvable. In this work, we present a novel reformulation strategy, in which we introduce sets of variables and constraints that represent the process of numerically solving the lower‐level problem based on a full step exact Hessian sequential quadratic programming method. The reformulated problem approximates a solution to the original one in the following sense: For a suitable number of imitated lower‐level iteration steps, the lower‐level problem is approximately solved in case a feasible point is found. The approach is illustrated by an example.