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 Zh. Vychisl. Mat. Mat. Fiz., 2012, Volume 52, Number 1, Pages 35–47 (Mi zvmmf9635)

Nonadaptive methods for polyhedral approximation of the Edgeworth–Pareto hull using suboptimal coverings on the direction sphere

A. V. Lotova, T. S. Maiskayab

a Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333 Russia
b Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119991 Russia

Abstract: For multicriteria convex optimization problems, new nonadaptive methods are proposed for polyhedral approximation of the multidimensional Edgeworth–Pareto hull (EPH), which is a maximal set having the same Pareto frontier as the set of feasible criteria vectors. The methods are based on evaluating the support function of the EPH for a collection of directions generated by a suboptimal covering on the unit sphere. Such directions are constructed in advance by applying an asymptotically effective adaptive method for the polyhedral approximation of convex compact bodies, namely, by the estimate refinement method. Due to the a priori definition of the directions, the proposed EPH approximation procedure can easily be implemented with parallel computations. Moreover, the use of nonadaptive methods considerably simplifies the organization of EPH approximation on the Internet. Experiments with an applied problem (from 3 to 5 criteria) showed that the methods are fairly similar in characteristics to adaptive methods. Therefore, they can be used in parallel computations and on the Internet.

Key words: nonadaptive methods of polyhedral approximation, Edgeworth–Pareto hull, suboptimal coverings, direction sphere

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English version:
Computational Mathematics and Mathematical Physics, 2012, 52:1, 31–42

Bibliographic databases:

UDC: 519.658
Revised: 14.07.2011

Citation: A. V. Lotov, T. S. Maiskaya, “Nonadaptive methods for polyhedral approximation of the Edgeworth–Pareto hull using suboptimal coverings on the direction sphere”, Zh. Vychisl. Mat. Mat. Fiz., 52:1 (2012), 35–47; Comput. Math. Math. Phys., 52:1 (2012), 31–42

Citation in format AMSBIB
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This publication is cited in the following articles:
1. G. K. Kamenev, A. V. Lotov, T. S. Mayskaya, “Iterative method for constructing coverings of the multidimensional unit sphere”, Comput. Math. Math. Phys., 53:2 (2013), 131–143
2. A. V. Lotov, “Decomposition of the problem of approximating the Edgeworth–Pareto hull”, Comput. Math. Math. Phys., 55:10 (2015), 1653–1664
3. A. V. Lotov, “Method for constructing an external polyhedral estimate of the trajectory tube for a nonlinear dynamic system”, Dokl. Math., 95:1 (2017), 95–98
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