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

Burla E. Ondes (bondespurdue.edu)
Susan R. Hunter (susanhunterpurdue.edu)

Abstract: We provide an upper bound on the Hausdorff distance between a Pareto set and its discretization in the context of bi-objective convex quadratic optimization on a compact feasible set. The upper bound is a least upper bound, calculated across all possible discretizations of the feasible set, for quadratic functions having spherical level sets. Our bound implies that if t is the dispersion of the observed points measured in the decision space, then the Hausdorff distance is O(sqrt(t)) as t decreases to zero.

Keywords: multi-objective optimization, Hausdorff distance, Pareto set approximation

Category 1: Other Topics (Multi-Criteria Optimization )

Category 2: Other Topics (Optimization of Simulated Systems )

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Entry Submitted: 05/17/2021
Entry Accepted: 05/17/2021
Entry Last Modified: 04/26/2022

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