Blood pressure (BP) is a significant controllable risk factor for cardiovascular disease (CVD), the leading cause of death worldwide. BP comprises two interrelated measurements: systolic and diastolic. CVD risk is minimized at intermediate BP values, a notion known as the J-curve effect. The J-curve effect imposes fundamental trade-offs in simultaneous management of systolic and diastolic BP; however, assessing a comprehensive set of joint systolic/diastolic BP treatment thresholds while explicitly considering the J-curve effect via randomized controlled trials (RCTs) is not feasible because of the time and cost-prohibitive nature of RCTs. In this study, we propose an analytics approach to identify promising joint systolic/diastolic BP threshold levels for antihypertensive treatment. More specifically, using one of the largest longitudinal BP progression data sets, we first build and fit Brownian motion processes to capture simultaneous progression of systolic/diastolic BP at the population level and externally validate our BP progression model on unseen data. We then analytically characterize the hazard ratio, which enables us to compute the optimal treatment decisions. Finally, building upon the optimal joint BP treatment thresholds, we devise a practical and easily implementable approximate policy. We estimate the potential impact of our findings through a simulation study, which indicates that the impact of explicitly considering the J-curve effect and joint systolic/diastolic BP in treatment decisions could be substantial. Specifically, we estimate that between approximately 3,000 and 9,000 premature deaths from cardiovascular disease in the United States could be prevented annually, a finding that could be tested empirically in randomized trials. This paper was accepted by Stefan Scholtes, healthcare management.