Explicit continuation methods and preconditioning techniques for unconstrained optimization problems
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This paper considers an explicit continuation method and the trust-region time-stepping scheme for the unconstrained optimization problem. Moreover, in order to improve its computational efficiency and robustness, the new method uses the switching preconditioning technique between the L-BFGS method and the inverse of the Hessian matrix. In the well-conditioned phase, the new method uses the L-BFGS method as the preconditioning technique in order to improve its computational efficiency. Otherwise, the new method uses the inverse of the Hessian matrix as the pre-conditioner in order to improve its robustness. We also analyze the global convergence analysis of the new method. According our numerical experiments, the new method is more robust and faster than the traditional optimization method such as the trust-region method and the line search method.
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