Convex Relaxations for Quadratic On/Off Constraints and Applications to Optimal Transmission Switching

This paper studies mixed-integer nonlinear programs featuring disjunctive constraints and trigonometric functions. We first characterize the convex hull of univariate quadratic on/off constraints in the space of original variables using perspective functions. We then introduce new tight quadratic relaxations for trigonometric functions featuring variables with asymmetrical bounds. These results are used to further tighten recent … Read more

Constraint Qualification Failure in Action

This note presents a theoretical analysis of disjunctive constraints featuring unbounded variables. In this framework, classical modeling techniques, including big-M approaches, are not applicable. We introduce a lifted second-order cone formulation of such on/off constraints and discuss related constraint qualification issues. A solution is proposed to avoid solvers’ failure. Citation H. L. Hijazi and L.Liberti … Read more

A Note on Linear On/Off Constraints

This note studies compact representations of linear on/off constraints in mixed-integer linear optimization. A characterization of the convex hull of linear disjunctions is given in the space of original variables. This result can improve formulations of mixed-integer linear programs featuring on/off constraints by reducing the integrality gap in a Branch and Bound approach. Citation @article{, … Read more