The extended horizontal linear complementarity problem: iterative methods and error analysis

Abstract: To the best of our knowledge, since the extended horizontal linear complementarity problem (EHLCP) was first introduced and studied by Kaneko in 1977, no iterative methods or error analysis have been developed for it due to the interdependence of its multiple unknowns in a 'chain-like' structure. This paper aims to address these gaps by: (1) proposing an equivalent fixed-point formulation of the EHLCP by using a variable transformation technique with the max-min function; (2) developing efficient iterative methods for solving the EHLCP based on this fixed-point form, along with their convergence analysis; (3) deriving global error bounds and computable estimates for the EHLCP. Several numerical examples from applications such as multicommodity market equilibrium and bilateral obstacle problems are given to demonstrate the effectiveness of the proposed methods and bounds.