This work presents a general method for linearizing bilinear terms in the upper level of bilevel optimization problems when the bilinear terms are products of the primal and dual variables of the lower level. Bilinear terms of this form often appear in energy market optimization models where the dual variable represents the market price of energy and the primal variable represents a generator dispatch decision. Prior works have linearized such bilinear terms for specific problems. This work is the first to demonstrate how to linearize these terms in the most general case.
Under review. Submitted August 24, 2021 to IEEE Transactions on Power Systems.