A Synthetic Approach to Multiobjective Optimization
نویسنده
چکیده
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.
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