In integrated digital image correlation (IDIC) methods attention must be paid to the influence of using a correct geometric and material model, but also to make the boundary conditions in the FE simulation match the real experiment. Another issue is the robustness and convergence of the IDIC algorithm itself, especially in cases when (FEM) simulations are slow. These two issues have been explored in this proceeding. The basis of the algorithm is the minimization of the residual. Different approaches for this minimization exist, of which a Gauss-Newton method is used most often. In this paper several other methods are presented as well and their performance is compared in terms of number of FE simulations needed, since this is the most time-consuming step in the iterative procedure. Beside method-specific recommendations, the main finding of this work is that, in practical use of IDIC, it is recommended to start using a very robust, but slow, derivative-free optimization method (e.g. Nelder-Mead) to determine the search direction and increasing the initial guess accuracy, while after some iterations, it is recommended to switch to a faster gradient-based method, e.g. (update-limited) Gauss-Newton.