Tikhonov regularization continuation methods and the trust-region updating strategy for linearly equality-constrained optimization problems

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. Otherwise, it uses the inverse of the regularization two-sided projected Hessian matrix as the pre-conditioner to improve its robustness. Numerical results also show that the new method is more robust and faster than the traditional optimization method such as the sequential quadratic programming (SQP), the alternating direction method of multipliers (ADMM) and the latest continuation method (Ptctr). The computational time of the new method is about one fifth of that of SQP for the large-scale problem. Finally, the global convergence analysis of the new method is also given.