This paper presents a quantitative framework to support policy decision-making around equitable energy interventions. By combining sociodemographic and techno-economic models in the energy space, we propose a linear programming model to calculate the optimal portfolio of energy investments that explicitly minimizes the energy burden of a given population of energy insecure households. The model is formulated as a multi-objective optimization suitable to support the decisions on weatherization and deployment of distributed energy resources. We illustrate our methodology with a case study involving a population of 14,043 energy insecure households in Wayne County, Detroit, United States.