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Zh. Vychisl. Mat. Mat. Fiz., 2009, Volume 49, Number 7, Pages 1184–1196 (Mi zvmmf4717)  

This article is cited in 8 scientific papers (total in 8 papers)

Optimality conditions and newton-type methods for mathematical programs with vanishing constraints

A. F. Izmailov, A. L. Pogosyan

Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119992, Russia

Abstract: A new class of optimization problems is discussed in which some constraints must hold in certain regions of the corresponding space rather than everywhere. In particular, the optimal design of topologies for mechanical structures can be reduced to problems of this kind. Problems in this class are difficult to analyze and solve numerically because their constraints are usually irregular. Some known first- and second-order necessary conditions for local optimality are refined for problems with vanishing constraints, and special Newton-type methods are developed for solving such problems.

Key words: mathematical program with vanishing constraints, mathematical program with complementarity constraints, constraint qualification, optimality conditions, sequential quadratic programming, active-set method.

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English version:
Computational Mathematics and Mathematical Physics, 2009, 49:7, 1128–1140

Bibliographic databases:

Document Type: Article
UDC: 519.626
Received: 14.11.2008

Citation: A. F. Izmailov, A. L. Pogosyan, “Optimality conditions and newton-type methods for mathematical programs with vanishing constraints”, Zh. Vychisl. Mat. Mat. Fiz., 49:7 (2009), 1184–1196; Comput. Math. Math. Phys., 49:7 (2009), 1128–1140

Citation in format AMSBIB
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\jour Comput. Math. Math. Phys.
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. F. Izmailov, A. L. Pogosyan, “A semismooth sequential quadratic programming method for lifted mathematical programs with vanishing constraints”, Comput. Math. Math. Phys., 51:6 (2011), 919–941  mathnet  crossref  mathscinet  isi
    2. Izmailov A.F., Pogosyan A.L., “Active-set Newton methods for mathematical programs with vanishing constraints”, Comput. Optim. Appl., 53:2 (2012), 425–452  crossref  mathscinet  zmath  isi  elib  scopus
    3. Dorsch D., Shikhman V., Stein O., “Mathematical programs with vanishing constraints: critical point theory”, J. Glob. Optim., 52:3 (2012), 591–605  crossref  mathscinet  zmath  isi  elib  scopus
    4. Hoheisel T., Kanzow Ch., Schwartz A., “Mathematical programs with vanishing constraints: a new regularization approach with strong convergence properties”, Optimization, 61:6 (2012), 619–636  crossref  mathscinet  zmath  isi  elib  scopus
    5. Achtziger W., Hoheisel T., Kanzow Ch., “A Smoothing-Regularization Approach to Mathematical Programs with Vanishing Constraints”, Comput. Optim. Appl., 55:3 (2013), 733–767  crossref  mathscinet  zmath  isi  elib  scopus
    6. Hu Q., Chen Yu., Zhu Zh., Zhang B., “Notes on Convergence Properties For a Smoothing-Regularization Approach To Mathematical Programs With Vanishing Constraints”, Abstract Appl. Anal., 2014, 715015  crossref  mathscinet  isi  scopus
    7. Mishra S.K., Singh V., Laha V., “On duality for mathematical programs with vanishing constraints”, Ann. Oper. Res., 243:1-2 (2016), 249–272  crossref  mathscinet  zmath  isi  elib  scopus
    8. Hu Q., Wang J., Chen Yu., Zhu Zh., “On an
      $$l_1$$
      l 1 exact penalty result for mathematical programs with vanishing constraints”, Optim. Lett., 11:3 (2017), 641–653  crossref  mathscinet  zmath  isi  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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