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Zh. Vychisl. Mat. Mat. Fiz., 2012, Volume 52, Number 6, Pages 990–998 (Mi zvmmf9615)  

This article is cited in 5 scientific papers (total in 5 papers)

Convergence analysis of two-phase methods for approximating the Edgeworth–Pareto hull in nonlinear multicriteria optimization problems

V. E. Berezkin, G. K. Kamenev

Dorodnitsyn Computing Centre of the Russian Academy of Sciences, Moscow

Abstract: The convergence of two-phase methods for approximating the Edgeworth–Pareto hull (EPH) in nonlinear multicriteria optimization problems is analyzed. The methods are based on the iterative supplement of the finite set of feasible criteria vectors (approximation basis) whose EPH approximates the desired set. A feature of two-phase methods is that the criteria images of randomly generated points of the decision space approach the Pareto frontier via local optimization of adaptively chosen convolutions of criteria. The convergence of two-phase methods is proved for both an abstract form of the algorithm and for a two-phase method based on the Germeier convolution.

Key words: multicriteria optimization, Pareto frontier, Edgeworth–Pareto hull, approximation method, two-phase method, convergence, statistical estimates

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English version:
Computational Mathematics and Mathematical Physics, 2012, 52:6, 846–854

Bibliographic databases:

UDC: 519.658
Received: 17.10.2011
Revised: 28.12.2011

Citation: V. E. Berezkin, G. K. Kamenev, “Convergence analysis of two-phase methods for approximating the Edgeworth–Pareto hull in nonlinear multicriteria optimization problems”, Zh. Vychisl. Mat. Mat. Fiz., 52:6 (2012), 990–998; Comput. Math. Math. Phys., 52:6 (2012), 846–854

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. G. K. Kamenev, “Study of convergence rate and efficiency of two-phase methods for approximating the Edgeworth–Pareto hull”, Comput. Math. Math. Phys., 53:4 (2013), 375–385  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    2. V. E. Berezkin, A. V. Lotov, E. A. Lotova, “Study of hybrid methods for approximating the Edgeworth–Pareto hull in nonlinear multicriteria optimization problems”, Comput. Math. Math. Phys., 54:6 (2014), 919–930  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    3. A. V. Lotov, A. I. Ryabikov, “Mnogokriterialnyi sintez optimalnogo upravleniya i ego primenenie pri postroenii pravil upravleniya kaskadom gidroelektrostantsii”, Tr. IMM UrO RAN, 20, no. 4, 2014, 187–203  mathnet  mathscinet  elib
    4. G. K. Kamenev, “Multicriteria identification sets method”, Comput. Math. Math. Phys., 56:11 (2016), 1843–1858  mathnet  crossref  crossref  isi  elib
    5. A. V. Lotov, “New external estimate for the reachable set of a nonlinear multistep dynamic system”, Comput. Math. Math. Phys., 58:2 (2018), 196–206  mathnet  crossref  crossref  isi  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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