Before revision: This paper considers the Tikhonv regularization continuation method and the trust-region updating strategy for the linearly equality-constrained optimization problem (Trcmtr). Moreover, in order to improve its computational efficiency and robustness, the new method uses the switching preconditioned technique. That is to say , the new method uses the L-BFGS method as the preconditioned technique to improve its computational efficiency in the well-posed phase .
After revision: This paper considers the Tikhonv regularization continuation method and the trust-region updating strategy for the linearly equality-constrained optimization problem . The proposed method utilizes the linear conservation law of the regularization method such that it does not need to compute the correction step for preserving the feasibility other than the previous continuation methods and the quasi-Newton updating formulas for the linearly equality-constrained optimization problem. Moreover , the new method uses the L-BFGS method as the preconditioned technique to improve its computational efficiency in the well-posed phase .