Feature selection is an important step in data preprocessing, which helps reducing the dimensionality of data and simplifying the models. This process not only reduces the computational complexity of models, but also improves their accuracy by eliminating irrelevant features and noise. The three most widely used approaches for feature selection are filter, wrapper and embedded methods. In this paper, first we review some support vector machine based Mixed-Integer Linear Programming (MILP) models and Supervised Infinite Feature Selection (Inf-FS$_s$) method. Then, we propose three hybrid approaches based on them. The first approach involves solving the relaxed linear model of the underlying MILP model and then solving the MILP model for those features with nonzero weights, namely a smaller MILP. In the second approach, first the Inf-FS$_s$ method is applied to rank the features. Then depending on the features costs, either chooses the top features from the ranked features until budget parameter is reached or solves a knapsack problem to select cost effective features. The third approach applies the first approach to the top $20\%$ of features ranked by Inf-FS$_s$ method. To evaluate the proposed approaches' performance, experiments are conducted on four high-dimensional benchmark datasets for fixed and random features costs. Results demonstrate that using either of the proposed approaches can significantly reduce running time of MILP models with comparable accuracies with the original MILP models.