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Zh. Vychisl. Mat. Mat. Fiz., 2007, Volume 47, Number 3, Pages 397–413 (Mi zvmmf313)  

This article is cited in 15 scientific papers (total in 15 papers)

Local search in problems with nonconvex constraints

T. V. Gruzdeva, A. S. Strekalovskii

Institute of System Dynamics and Control Theory, Siberian Division, Russian Academy of Sciences, ul. Lermontova 134, Irkutsk, 664033, Russia

Abstract: Nonconvex optimization problems with an inequality constraint given by the difference of two convex functions (by a d.c. function) are considered. Two methods for finding local solutions to this problem are proposed that combine the solution of partially linearized problems and descent to a level surface of the d.c. function. The convergence of the methods is analyzed, and stopping criterions are proposed. The methods are compared by testing them in a numerical experiment.

Key words: difference of two convex functions, local search, linearized problem, level surface, critical point.

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English version:
Computational Mathematics and Mathematical Physics, 2007, 47:3, 381–396

Bibliographic databases:

UDC: 519.852.6
Received: 07.08.2006

Citation: T. V. Gruzdeva, A. S. Strekalovskii, “Local search in problems with nonconvex constraints”, Zh. Vychisl. Mat. Mat. Fiz., 47:3 (2007), 397–413; Comput. Math. Math. Phys., 47:3 (2007), 381–396

Citation in format AMSBIB
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\by T.~V.~Gruzdeva, A.~S.~Strekalovskii
\paper Local search in problems with nonconvex constraints
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2007
\vol 47
\issue 3
\pages 397--413
\mathnet{http://mi.mathnet.ru/zvmmf313}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2348290}
\zmath{https://zbmath.org/?q=an:05200989}
\transl
\jour Comput. Math. Math. Phys.
\yr 2007
\vol 47
\issue 3
\pages 381--396
\crossref{https://doi.org/10.1134/S0965542507030049}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34247159679}


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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. T. V. Gruzdeva, “Reshenie zadachi o klike svedeniem k zadache s d. c. ogranicheniem”, Diskretn. analiz i issled. oper., 15:6 (2008), 20–33  mathnet  mathscinet  zmath
    2. T. V. Gruzdeva, E. G. Petrova, “Numerical solution of a linear bilevel problem”, Comput. Math. Math. Phys., 50:10 (2010), 1631–1641  mathnet  crossref  adsnasa  isi
    3. Strekalovsky A.S., Orlov A.V., Malyshev A.V., “On computational search for optimistic solutions in bilevel problems”, J. Global Optim., 48:1 (2010), 159–172  crossref  mathscinet  zmath  isi  elib  scopus
    4. Gruzdeva T.V., Strekalovskii A.S., Orlov A.V., Druzhinina O.V., “Negladkie zadachi minimizatsii raznosti dvukh vypuklykh funktsii”, Vychislitelnye metody i programmirovanie: novye vychislitelnye tekhnologii, 12:1 (2011), 384–396  mathnet  elib
    5. Gruzdeva T.V., “Zadacha sfericheskoi binarnoi otdelimosti”, Izvestiya Irkutskogo gos. un-ta. Ser. Matematika, 5:3 (2012), 18–31  zmath  elib
    6. T. V. Gruzdeva, “Zadacha sfericheskoi binarnoi otdelimosti”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 5:3 (2012), 18–31  mathnet
    7. Gruzdeva T.V., “On a Continuous Approach for the Maximum Weighted Clique Problem”, J. Glob. Optim., 56:3, SI (2013), 971–981  crossref  mathscinet  zmath  isi  elib  scopus
    8. Strekalovsky A.S., “on Local Search in D.C. Optimization Problems”, Appl. Math. Comput., 255 (2015), 73–83  crossref  mathscinet  zmath  isi  elib  scopus
    9. Gaudioso M., Gruzdeva T.V., Strekalovsky A.S., “On numerical solving the spherical separability problem”, J. Glob. Optim., 66:1, SI (2016), 21–34  crossref  mathscinet  zmath  isi  elib  scopus
    10. Gruzdeva T., Strekalovsky A., “An Approach to Fractional Programming via D.C. Constraints Problem: Local Search”, Discrete Optimization and Operations Research, Lecture Notes in Computer Science, 9869, eds. Kochetov Y., Khachay M., Beresnev V., Nurminski E., Pardalos P., Springer Int Publishing Ag, 2016, 404–417  crossref  mathscinet  zmath  isi  scopus
    11. Strekalovsky A.S., “On the Merit and Penalty Functions for the D.C. Optimization”, Discrete Optimization and Operations Research, Lecture Notes in Computer Science, 9869, eds. Kochetov Y., Khachay M., Beresnev V., Nurminski E., Pardalos P., Springer Int Publishing Ag, 2016, 452–466  crossref  mathscinet  zmath  isi  scopus
    12. Gruzdeva T.V., Ushakov A.V., Enkhbat R., “A Biobjective Dc Programming Approach to Optimization of Rougher Flotation Process”, Comput. Chem. Eng., 108 (2017), 349–359  crossref  isi  scopus
    13. Strekalovsky A.S., Minarchenko I.M., “A Local Search Method For Optimization Problem With D.C. Inequality Constraints”, Appl. Math. Model., 58 (2018), 229–244  crossref  mathscinet  isi  scopus
    14. Gruzdeva T.V., Strekalovsky A.S., “On Solving the Sum-of-Ratios Problem”, Appl. Math. Comput., 318 (2018), 260–269  crossref  mathscinet  isi  scopus
    15. Gadhi N.A., Dempe S., “Sufficient Optimality Conditions For a Bilevel Semivectorial Dc Problem”, Numer. Funct. Anal. Optim., 39:15 (2018), 1622–1634  crossref  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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