The matching and interaction between the impeller and vaned diffuser is the most important aerodynamic-coupling between the components of a high-speed centrifugal compressor. Many research studies have been carried out during the last decade, both experimentally and numerically, on the flow mechanisms underlying impeller–vaned diffuser matching and interaction, with the aim of achieving a high-performance stage. However, the published work lacks any study that optimizes the matching of the impeller–vaned diffuser components in the environment of a full compressor stage due to two unresolved issues, i.e., identifying an effective matching optimization strategy and the high dimensional nature of the problem. To tackle these difficulties, four different optimization strategies (i.e., (1) integrated, (2) single component, (3) parallel, and (4) sequential optimization strategies) have been proposed and validated through a high dimensional matching optimization of the Radiver compressor test case published by the Institute of Jet Propulsion and Turbomachinery at Rheinisch-Westfälische Technische Hochschule (RWTH) Aachen University. Particular attention has been paid to the slope of the diffuser total pressure ratio characteristic near the surge point to further extend the stage surge margin. The results showed that the integrated optimization strategy was the most effective one for achieving good matching of the impeller–vaned diffuser interaction due to its inherently strong coupling optimization. Compared with the baseline compressor, the optimized stage achieved a gain of 1.2% in total-to-total isentropic efficiency at the peak efficiency point as well as a predicted 26.17% increase in stable operating range. For the stage examined in this study, a fore-loaded design of impeller blade as well as an increased vane angle for the diffuser vane was beneficial to the impeller–vaned diffuser matching. The more uniform spanwise distributions of the impeller discharge flow angle and the diffuser vane incidence presented the opportunity for a more optimized matching of the flow field between the 3D impeller and the 2D vaned diffuser. The outcomes of this work are particularly relevant for the advanced design of high-speed centrifugal compressors.