The anisotropic mechanical response of metallic materials can be modeled using crystal plasticity, which resolves plastic slip on individual crystallographic systems. For rate-independent formulations, the non-uniqueness of active slip systems presents significant computational challenges, necessitating robust numerical solution strategies [1]. Interior point methods have gained attention as an effective framework for addressing these challenges. Logarithmic barrier functions are typically employed to account for inequality constraints by penalizing the objective function [2,3]. By progressively decreasing the barrier parameter and applying Newton's method, one can recover the solution to the original problem. However, the conventional implementation of interior point methods is computationally expensive due to its two-level structure. In this structure, an outer iteration controls the reduction of the barrier parameter, and an inner iteration solves each barrier subproblem. This architecture prevents warm-starting within finite element simulations. Our approach addresses this issue by keeping the barrier parameter constant and using solution data from prior load increments to initialize the interior point algorithm. Through numerical investigations at the integration point level and within full finite element simulations, we demonstrate that this strategy significantly improves computational efficiency and algorithmic robustness. [1] C. Miehe and J. Schröder. A comparative study of stress update algorithms for rate-independent and rate-dependent crystal plasticity. International Journal for Numerical Methods in Engineering, 50:273–298, 2001. [2] L. Scheunemann, P. Nigro, J. Schröder, and P. Pimenta. A novel algorithm for rate independent small strain crystal plasticity based on the infeasible primal-dual interior point method. International Journal of Plasticity, 124:1–19, 2020. [3] A. Niehüser and J. Mosler. Numerically efficient and robust interior-point algorithm for finite strain rate-independent crystal plasticity. Computer Methods in Applied Mechanics and Engineering, vol. 416, p. 116392, 2023.