In Chap. 7 , we use the smooth function instead of KKT conditions to reformulate the non-smooth elastoplastic problem into a system of smooth nonlinear equations. In numerical optimization, the problem of nonlinear equations is equivalent to an unconstrained minimization problem of a merit function that is constructed by nonlinear equations. The solution of nonlinear equations corresponds to the minimum point of a merit function in multidimensional space. Numerical optimization algorithms such as line search and trust region methods can solve unconstrained minimization problems with strong nonlinear characteristics more effectively. This chapter develops two robust unconstrained stress update algorithms by combining numerical optimization methods with unconstrained stress update strategies. The MCC model is used as an application object for these two algorithms. The unconstrained minimization problem corresponding to the nonlinear stress integral equations is solved separately through the inexact LSM and NMTR method, ensuring the convergence of the iterative solution under large load step size and strong nonlinear cases. Based on the proposed algorithms, the MCC model is numerically implemented in ABAQUS software by the UMAT subroutine. The performance of the algorithms is further evaluated through numerical analysis at the integration point level and structural level.