Journal
SIAM JOURNAL ON OPTIMIZATION
Volume 21, Issue 2, Pages 463-490Publisher
SIAM PUBLICATIONS
DOI: 10.1137/100784746
Keywords
Multiobjective optimization; multicriteria optimization; Pareto critical set; Delaunay tessellations in general dimension; stability of mappings
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We propose a strategy for approximating Pareto optimal sets based on the global analysis framework proposed by Smale [Global analysis and economics. I. Pareto optimum and a generalization of Morse theory, in Dynamical Systems, Academic Press, New York, 1973, pp. 531-544]. The method highlights and exploits the underlying manifold structure of the Pareto sets, approximating Pareto optima by means of simplicial complexes. The method distinguishes the hierarchy between singular set, Pareto critical set, and stable Pareto critical set, and it can handle the problem of superposition of local Pareto fronts, occurring in the general nonconvex case. Furthermore, a quadratic convergence result in a suitable setwise sense is proven and tested in a number of numerical examples.
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