New SRQP Method for Solving Nonlinear Complementarity Problems

Abstract

Extending the framework developed in [5], this study introduces a refined variant of the square root quadratic proximal (SRQP) method for the resolution of nonlinear complementarity problems. Unlike the conjugate gradient scheme adopted in [5], which constructs search directions through a combination of current and preceding iterates, the proposed approach incorporates a simplified correction mechanism that avoids such combinations. Under the assumption that the mapping \(F\) is pseudomonotone, the global convergence of the method is rigorously established. Furthermore, preliminary numerical experiments are reported to assess the efficiency and robustness of the proposed algorithm.