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Cybernetics and Systems Analysis

, Volume 52, Issue 1, pp 85–95 | Cite as

Exact Penalty Functions and Convex Extensions of Functions in Schemes of Decomposition in Variables*

Article

Abstract

Using exact penalty functions in schemes of decomposition in variables for nonlinear optimization make it possible to overcome problems related to implicit description of the feasible region of master problem. The paper deals with determining the values of penalty coefficients in such an approach. In the case where the functions of the original problem are not defined on the whole space of variables, the author proposes to use convex extension of functions.

Keywords

convex programming exact penalty functions decomposition methods 

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References

  1. 1.
    N. Z. Shor, Nondifferentiable Optimization and Polynomial Problems, Kluwer Acad. Publ., London (1998).CrossRefMATHGoogle Scholar
  2. 2.
    V. Zverovich, C. Fábián, E. Ellison, and G. Mitra, “A computational study of a solver system for processing two-stage stochastic LPs with enhanced Benders decomposition,” Math. Program. Comput., 4, Issue 3, 211–238 (2012).Google Scholar
  3. 3.
    A. Ruszczynski, “A regularized decomposition method for minimizing a sum of polyhedral functions,” Math. Program., 35, 309–333 (1986).MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Yu. P. Laptin, “ε-subgradients in methods of decomposition in variables for some optimization problems,” Teoriya Optym. Rishen’, No. 2, 75–82 (2003).Google Scholar
  5. 5.
    Yu. P. Laptin and N. G. Zhurbenko, “Certain questions in solving block nonlinear optimization problems with coupling variables,” Cybern. Syst. Analysis, 42, No. 2, 202–208 (2006).MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    R. H. Byrd, G. Lopez-Calva, and J. Nocedal, “A line search exact penalty method using steering rules,” Math. Program., Series A and B, 133, 39–73 (2012).Google Scholar
  7. 7.
    B. N. Pshenichnyi, Convex Analysis and Extremum Problems [in Russian], Nauka, Moscow (1980).MATHGoogle Scholar
  8. 8.
    Yu. M. Danilin, “Linearization and penalty functions,” Cybern. Syst. Analysis, 38, No. 5, 691–702 (2002).MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Yu. P. Laptin and A. P. Likhovid, “Using convex extensions of functions to solve nonlinear optimization problems,” Upravl. Sist. Mash., No. 6, 25–31 (2010).Google Scholar
  10. 10.
    Yu. P. Laptin and T. A. Bardadym, “Some approaches to regularization of nonlinear optimization problems,” J. Autom. Inform. Sci., 43, No. 5, 40–51 (2011).CrossRefGoogle Scholar
  11. 11.
    Yu. P. Laptin, “Construction of exact penalty functions,” Vestnik S.-Peterburg. Univ., Series 10: Applied Mathematics, Issue 4, 21–31 (2013).Google Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.V. M. Glushkov Institute of CyberneticsNational Academy of Sciences of UkraineKyivUkraine

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