To address traditional linear discriminant analysis’s insufficient robustness to noise and poor generalization performance on high-dimensional datasets with small sample sizes (i.e., where the number of features far exceeds the number of samples), literature proposed robust linear discriminant analysis (RLDA) and robust sparse linear discriminant analysis (RSLDA), along with an ADMM-based optimization algorithm for solving them. However, this method lacks convergence guarantees and fails to converge on some datasets. Based on the structural features of RLDA and RSLDA, an improved optimization algorithm DC_SLDA based on differences of convex functions (DC) programming is proposed. The algorithm transforms the original problem into a DC programming problem through DC decomposition, and then applies the difference of convex functions algorithm for iterative solution. The algorithm proposed not only has convergence guarantees but also features closed-form solutions for its subproblems, which significantly improves the training efficiency of the model.