A SYNTHETIC APPROACH TO MULTIOBJECTIVE OPTIMIZATION
Alberto Lovison · arXiv (Cornell University) · 2010
We propose a strategy for approximating Pareto optimal sets based on the global analysis framework proposed by Smale (Dynamical systems, Academic Press, New York (1973) 531{ 544). We speak about synthetic approach because the optimal set is natively approximated by means of a compound geometrical object, i.e., a simplicial complex, rather than by an unstructured scatter of individual optima. The method distinguishes the hierarchy between singular set, Pareto critical set and stable Pareto critical set. Furthermore, a quadratic convergence result in set wise sense is proven and tested over numerical examples.