Abstract：Recognized as an important way to ensure the stability of underground chambers，prestressed anchor cables are widely used in underground engineering. There is an initial stress after the prestressed anchor cable is installed，and the stress varies with the consequence of excavation. How to select an appropriately initial tensile tonnage to make the stress of prestressed anchor cable reach the designed stress so as not only to exert the effect of prestressed cable but also to preserve a certain of safety margin is an important issue. The issue is converted to an optimization problem on reasonable tensile coefficient of prestressed anchor cable. Firstly，stress calculation theory of prestressed anchor cable is introduced. Then，the optimal self-adjusting variable-metric algorithm using difference coefficients and imprecise linear search is proposed and applied to inversion of reasonable tensile coefficient of prestressed anchor cable. The algorithm improves the conventional variable-metric method by using self-adjusting variable-metric method based on Broyden¢s family to update metric matrix，makes different coefficients approach gradient and imprecise linear search method find optimal step length. At the same time，by using incremental variable plastic stiffness matrix method，reassembling stiffness matrix is avoided when prestress is modified，consequently computing speed is improved. A case study is given at last，which proves that the algorithm¢s superiorities of super-linear convergence，less computation，and better numerical stability.
