Abstract
Estimation Refinement (ER) is an adaptive method for polyhedral approximations of multidimensional convex sets. ER is used in the framework of the Interactive Decision Maps (IDM) technique that provides interactive visualization of the Pareto frontier for convex sets of feasible criteria vectors. We state that, for ER, the number of facets of approximating polytopes is asymptotically multinomial of an optimal order. Furthermore, the number of support function calculations, needed to be resolved during the approximation, and which complexity is unknown beforehand since a user of IDM provides his own optimization algorithm, is bounded from above by a linear function of the number of iterations.
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Efremov, R., Kamenev, G. (2009). Optimality of the Methods for Approximating the Feasible Criterion Set in the Convex Case. In: Barichard, V., Ehrgott, M., Gandibleux, X., T'Kindt, V. (eds) Multiobjective Programming and Goal Programming. Lecture Notes in Economics and Mathematical Systems, vol 618. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85646-7_3
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DOI: https://doi.org/10.1007/978-3-540-85646-7_3
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