An infeasibility certificate for non-linear programming based on pareto-criticality conditions

Abstract

This thesis proposes a new necessary condition for the infeasibility of non-linear optimization problems (that becomes necessary under convexity assumption) which is stated as a Pareto-criticality condition of an auxiliary multiobjective optimization problem. This condition can be evaluated, in a given problem, using multiobjective optimization algorithms, in a search that either leads to a feasible point or to a point in which the infeasibility conditions holds. The resulting infeasibility certificate, which is built with primal variables only, has global validity in convex problems and has at least a local meaning in generic nonlinear optimization problems. In the case of noisy problems, in which gradient information is not available, the proposed condition can still be employed in a heuristic flavor, as a by-product of the expected features of the Pareto-front of the auxiliary multiobjective problem.