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Optimality of the Methods for Approximating the Feasible Criterion Set in the Convex Case

In: Multiobjective Programming and Goal Programming

Author

Listed:
  • Roman Efremov

    (Rey Juan Carlos University)

  • Georgy Kamenev

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.

Suggested Citation

  • Roman Efremov & Georgy Kamenev, 2009. "Optimality of the Methods for Approximating the Feasible Criterion Set in the Convex Case," Lecture Notes in Economics and Mathematical Systems, in: Vincent Barichard & Matthias Ehrgott & Xavier Gandibleux & Vincent T'Kindt (ed.), Multiobjective Programming and Goal Programming, pages 25-33, Springer.
    • Handle: RePEc:spr:lnechp:978-3-540-85646-7_3
    DOI: 10.1007/978-3-540-85646-7_3
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