Tittle: Anderson accelerating the preconditioned modulus approach for linear complementarity problems on second-order cones
Abstract: Second-order cone linear complementarity problems (SOCLCPs) have wide applications in real world, and the latest modulus method is proved to be an efficient solver. Here, inspired by the state-of-the-art modulus method and Anderson acceleration (AA), we construct the Anderson accelerating preconditioned modulus (AA+PMS) approach. Theoretically, in the first stage, we utilize the Frechet-differentiability of the absolute value function in Jordan algebra to explore its new properties. On this basis, we establish the convergence theory for the PMS approach different from the previous analysis, and further discuss the selection strategy of parameters involved. In the second stage, we demonstrate the strong semi-smoothness of the absolute value function in Jordan algebra and, thus, establish the local convergence theory for the AA+PMS approach. Finally, we conduct rich numerical experiments with application to some well-structured examples, the second-order cone programming, the Signorini problem of the Laplacian and the three-dimensional frictional contact problem to verify the robustness and effectiveness of the AA+PMS approach.
Citation: Li, Z., Zhang, H., Jin, Y. et al. Anderson accelerating the preconditioned modulus approach for linear complementarity problems on second-order cones. Numer Algor 91, 803–839 (2022).
