Approximating Pareto curves using the hyper-ellipse
Yusheng Li, Georges M. Fadel, Margaret M. Wiecek · 7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization · 1998
This paper proposes an approximation method to generate the set of Pareto solutions of bi-criteria convex optimization problems. The approximation is achieved by means of fitting a hyper-ellipse to a very small number of Pareto points and the equation of hyperellipse yields an explicit analytical description of the Pareto set. The method is applied to unconstrained and constrained problems, and illustrated on examples showing its efficiency. The paper identifies the limits of applicability of the approach and proposes further extensions.