{"ID":2849819,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.23791","arxiv_id":"2510.23791","title":"A Family of Convex Models to Achieve Fairness through Dispersion Control","abstract":"Controlling the dispersion of a subset of decision variables in an optimization problem is crucial for enforcing fairness or load-balancing across a wide range of applications. Building on the well-known equivalence of finite-dimensional norms, the article develops a family of parameterized convex models that regulate the dispersion of a vector of decision-variable values through its coefficient of variation. Each model has a single parameter taking values in the interval $[0,1]$. When the parameter is set to zero, the model imposes only a trivial constraint on the optimization problem; when set to one, it enforces equality of all the decision variables. As the parameter varies, the coefficient of variation is provably bounded above by a monotonic function of that parameter. The article also presents theoretical results relating the space of feasible solutions across all models. Finally, it compares the models' solution quality on a variant of the assignment problem that regulates the dispersion in the assignment costs.","short_abstract":"Controlling the dispersion of a subset of decision variables in an optimization problem is crucial for enforcing fairness or load-balancing across a wide range of applications. Building on the well-known equivalence of finite-dimensional norms, the article develops a family of parameterized convex models that regulate...","url_abs":"https://arxiv.org/abs/2510.23791","url_pdf":"https://arxiv.org/pdf/2510.23791v4","authors":"[\"Abhay Singh Bhadoriya\",\"Deepjyoti Deka\",\"Kaarthik Sundar\"]","published":"2025-10-27T19:20:54Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}