<p>The sparse index tracking problem centers on the development of a sparse portfolio strategy aimed at tracking predefined financial indices. This approach is highly valued for its capacity to reduce transaction costs and improve the efficiency of management processes. In this study, we introduce two novel cardinality-constrained index tracking models designed to yield sparse portfolios. The first model imposes a cardinality constraint to restrict the number of assets in the portfolio to a predefined quantity or fewer. The second model builds upon this by incorporating cardinality constraints that apply to both the portfolio composition and its turnover. To address the proposed models, we develop an inertial block proximal alternating linearized minimization algorithm, which integrates the inertial technique with block coordinate descent. The convergence of this method is rigorously established. Furthermore, we conduct numerical experiments on several financial datasets, and the empirical results demonstrate the superior performance of the proposed models and algorithms across multiple financial metrics, notably in achieving sparse portfolios.</p>