An Upper Bound on the Hausdorff Distance Between a Pareto Set and its Discretization in Bi-Objective Convex Quadratic Optimization

We provide upper bounds on the Hausdorff distances between the efficient set and its discretization in the decision space, and between the Pareto set (also called the Pareto front) and its discretization in the objective space, in the context of bi-objective convex quadratic optimization on a compact feasible set. Our results imply that if t is the dispersion of the sampled points in the discretized feasible set, then the Hausdorff distances in both the decision space and the objective space are O(sqrt(t)) as t decreases to zero.


Ondes, B.E., Hunter, S.R. An upper bound on the Hausdorff distance between a Pareto set and its discretization in bi-objective convex quadratic optimization. Optim Lett 17, 45–74 (2023).