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Alzheimer's disease (AD) is a serious neurodegenerative condition that affects millions of people across the world. Recently machine learning models have been used to predict the progression of AD, although they frequently do not take advantage of the longitudinal and structural components associated with multi-modal medical data. To address this, we present a new algorithm that uses the multi-block alternating direction method of multipliers to optimize a novel objective that combines multi-modal longitudinal clinical data of various modalities to simultaneously predict the cognitive scores and diagnoses of the participants in the Alzheimer's Disease Neuroimaging Initiative cohort. Our new model is designed to leverage the structure associated with clinical data that is not incorporated into standard machine learning optimization algorithms. This new approach shows state-of-the-art predictive performance and validates a collection of brain and genetic biomarkers that have been recorded previously in AD literature.