The regularization continuation method with an adaptive time step control for linearly equality-constrained optimization problems

This paper considers the 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 preconditioning technique to improve its computational efficiency in the well-posed phase, and 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 and the recent continuation method. Finally, the global convergence analysis of the new method is also given.