Inverse optimization is an area of study where the purpose is to infer the unknown parameters of an optimization problem when a set of observations is available on the previous decisions made in the settings of the problem. We develop a framework to effectively and efficiently infer the cost vector of a linear optimization problem based on multiple observations on the decisions made previously.
We then test our models in the setting of a diet problem on a data-set obtained from NHANES; The data-set is accessible via the link bellow: