A self-adaptive extragradient–CQ method for a class of bilevel split equilibrium problem with application to Nash Cournot oligopolistic electricity market models

Van Quy (Optimization 68(4):753–771, 2018) established an extragradient–CQ algorithm for solving a class of bilevel split equilibrium problem. The step-size in the algorithm requires computation of a certain matrix norm which is costly. Moreover, bilevel problems often possess huge number of constraints and possibly require a robust and adaptive step-size algorithm to withstand failure in instances of real-world problems with large data sizes. In this paper, we propose a self-adaptive step-size extragradient–CQ algorithm for solving the same problem without prior knowledge of operator norm and provide a numerical example to demonstrate the effectiveness of our method.