A sequential linear complementarity problem method for generalized Nash equilibrium problems

Abstract: We propose a sequential linear complementarity problem (SLCP) method for solving generalized Nash equilibrium problems (GNEPs). By introducing a novel merit function that utilizes the specific structure of GNEPs, we establish global convergence of the method. The conditions guaranteeing global convergence are analogous to those for the classical sequential quadratic programming method with exact Lagrange Hessians, making this a natural and reasonable generalization. Moreover, we provide a detailed analysis of the solvability of the mixed linear complementarity subproblems, which are formulated as affine GNEPs. Sufficient characterizations for the local superlinear convergence are also derived, highlighting the efficiency of the proposed method. Finally, numerical experiments demonstrate the practical performance and effectiveness of the SLCP method in comparison with existing approaches.