A new smoothing Broyden-like method for solving the mixed complementarity problem with a \(P_{0}\)-function
In this paper, the authors propose a new smoothing Broyden-like algorithm for solving the mixed complementarity problem (MCP) based on a new perturbed mid function. The algorithm considered here combines the advantages of quasi-Newton method of local superlinear convergence and a floating genetic algorithm in group search, and global convergence. In addition, existence and continuity of a smooth path for solving the mixed complementarity problem with a \(P_0\)-function are discussed in this paper. The authors also show that, under suitable conditions, the iterates generated by the proposed method converge globally to a solution of the mixed complementarity problem. Finally, making use of smooth and semismooth techniques, the authors prove the local superlinear convergence of the proposed algorithm under mild assumptions. Some numerical results are reported to show that the new method is feasible and effective.
scientific article; zbMATH DE number 5757783
scientific article