Alzheimer’s disease (AD) is the most common type of dementia and will be an increasing health problem in society as the population ages. Mild cognitive impairment (MCI) is considered to be a prodromal stage of AD. The ability to identify subjects with MCI will be increasingly important as disease modifying therapies for AD are developed. We propose a semi-supervised learning method based on robust optimization for the identification of MCI from [18F]Fluorodeoxyglucose PET scans. We extracted three groups of spatial features from the cortical and subcortical regions of each FDG-PET image volume. We measured the statistical uncertainty related to these spatial features via transformation using an incomplete random forest and formulated the MCI identification problem under a robust optimization framework. We compared our approach to other state-of-the-art methods in different learning schemas. Our method outperformed the other techniques in the ability to separate MCI from normal controls.