A Novel Neurodynamic Approach to Bilevel Quadratic Programming

In this study, we convert a bilevel quadratic programming problem (BQPP) into single-level mathematical programming with complementary constraints (MPCC), utilizing the Karush-Kuhn-Tucker (KKT) theorem. We address the inherent nonconvexity of MPCC by applying the linear transformation, which effectively relaxes the complementary slackness conditions to semi-positive definite quadratic constraints, thereby facilitating the transformation of the problem into convex programming. Furthermore, we introduce a projection neural network designed for resolving the MPCC efficiently. This neural network is structured to guarantee convergence from any initial point to the optimal solution of the original problem. The efficacy of our methodology is validated through a numerical simulation.