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Zh. Vychisl. Mat. Mat. Fiz., 2011, Volume 51, Number 1, Pages 3–23 (Mi zvmmf8042)  

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

On the limiting properties of dual trajectories in the Lagrange multipliers method

A. F. Izmailov

Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119991 Russia

Abstract: For the method of Lagrange multipliers (i.e., augmented Lagrangians), possible and typical scenarios for the asymptotic behavior of dual trajectories are examined in the case where the Lagrange multiplier is nonunique. The influence of these scenarios on the convergence rate is also investigated.

Key words: mathematical programming problem, augmented Lagrangian, method of multipliers, superlinear convergence, critical Lagrange multiplier.

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English version:
Computational Mathematics and Mathematical Physics, 2011, 51:1, 1–20

Bibliographic databases:

Document Type: Article
UDC: 519.926
Received: 09.08.2010

Citation: A. F. Izmailov, “On the limiting properties of dual trajectories in the Lagrange multipliers method”, Zh. Vychisl. Mat. Mat. Fiz., 51:1 (2011), 3–23; Comput. Math. Math. Phys., 51:1 (2011), 1–20

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. A. F. Izmailov, E. I. Uskov, “On the influence of the critical Lagrange multipliers on the convergence rate of the multiplier method”, Comput. Math. Math. Phys., 52:11 (2012), 1504–1519  mathnet  crossref  mathscinet  isi  elib  elib
    2. Pei Y., Ye Ch., Liu L., “Inventory-transportation integrated optimization problem in many-to-many distribution network”, Sustainable Environment and Transportation, Applied Mechanics and Materials, 178-181, eds. Chu M., Xu H., Jia Z., Fan Y., Xu J., Trans. Tech. Publications Ltd., 2012, 1965–1969  crossref  isi  scopus
    3. Izmailov A.F. Solodov M.V., “Critical Lagrange Multipliers: What We Currently Know About Them, How They Spoil Our Lives, and What We Can Do About It”, Top, 23:1 (2015), 1–26  crossref  mathscinet  zmath  isi  scopus
    4. Izmailov A.F. Solodov M.V. Uskov E.I., “Combining Stabilized Sqp With the Augmented Lagrangian Algorithm”, Comput. Optim. Appl., 62:2 (2015), 405–429  crossref  mathscinet  zmath  isi  elib  scopus
    5. Izmailov A.F., Uskov E.I., “Attraction of Newton Method To Critical Lagrange Multipliers: Fully Quadratic Case”, Math. Program., 152:1-2 (2015), 33–73  crossref  mathscinet  zmath  isi  elib  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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