An infeasibility certificate for nonlinear programming based on Pareto criticality condition

This paper proposes a new necessary condition for the infeasibility of nonlinear optimization problems, that becomes also sufficient under a convexity assumption, which is stated as a Pareto-criticality condition of an auxiliary multi-objective optimization problem. This condition is evaluated in a search that either leads to a feasible point or to a point at which the infeasibility conditions hold. The resulting infeasibility certificate has global validity in convex problems and has at least a local meaning in generic nonlinear problems.