Explicit pseudo-transient continuation and the trust-region updating strategy for unconstrained optimization
Abstract
This paper considers an explicit continuation method and the trust-region updating strategy for the unconstrained optimization problem. Moreover, in order to improve its computational efficiency and robustness, the new method uses the switching preconditioning technique. 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. Numerical results aslo show that the new method is more robust and faster than the traditional optimization method such as the trust-region method and the line search method. The computational time of the new method is about one percent of that of the trust-region method (the subroutine fminunc.m of the MATLAB2019a environment, it is set by the trust-region method) or one fifth of that the line search method (fminunc.m is set by the quasi-Newton method) for the large-scale problem. Finally, the global convergence analysis of the new method is also given.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2020
- DOI:
- 10.48550/arXiv.2012.14808
- arXiv:
- arXiv:2012.14808
- Bibcode:
- 2020arXiv201214808L
- Keywords:
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- Mathematics - Optimization and Control;
- Mathematics - Dynamical Systems;
- Mathematics - Numerical Analysis