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

• The proposed method utilizes the linear conservation law of regularization continuation such that it does not need to compute correction step for preserving feasibility other than previous methods and quasi-Newton updating formulas. replaces pre-conditioner with inverse two-sided projection Lagrangian Hessian as pre- conditioner improve its robustness in ill-posed phase. This paper considers trust-region strategy optimization problem equality constraints. formulas linearly constrained problem. Moreover, new uses special limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) formula preconditioning technique computational efficiency well-posed phase, regularized robustness. Numerical results also show is more robust faster traditional alternating direction multipliers (ADMM), sequential quadratic programming (SQP) (the built-in subroutine fmincon.m MATLAB2020a environment), recent (Ptctr). time about 1/3 SQP (fmincon.m). Finally, global convergence analysis given.