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International Conference on Discrete Optimization and Operations Research

DOOR 2016: Discrete Optimization and Operations Research pp 452–466Cite as

On the Merit and Penalty Functions for the D.C. Optimization

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9869))

Abstract

This paper addresses a rather general problem of nonlinear optimization with the inequality constraints and the goal function defined by the (d.c.) functions represented by the difference of two convex functions. In order to reduce the constrained optimization problem to an unconstrained one, we investigate three auxiliary problems with the max-merit, Lagrange and penalty goal functions. Further, their relations to the original problem are estimated by means of the new Global Optimality Conditions and classical Optimization Theory as well as by examples.

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Acknowledgments

This work has been supported by the Russian Science Foundation, project No. 15-11-20015.

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Authors and Affiliations

  1. Institute for System Dynamics and Control Theory SB RAS, Lermontov street, 134, Irkutsk, 664033, Russia

    Alexander S. Strekalovsky

Authors
  1. Alexander S. Strekalovsky
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Correspondence to Alexander S. Strekalovsky .

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Editors and Affiliations

  1. Sobolev Institute of Mathematics , Novosibirsk, Russia

    Yury Kochetov

  2. Krasovsky Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Michael Khachay

  3. Sobolev Institute of Mathematics , Novosibirsk, Russia

    Vladimir Beresnev

  4. Far Eastern Federal University , Vladivostik, Russia

    Evgeni Nurminski

  5. University of Florida , Gainesville, Florida, USA

    Panos Pardalos

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Strekalovsky, A.S. (2016). On the Merit and Penalty Functions for the D.C. Optimization. In: Kochetov, Y., Khachay, M., Beresnev, V., Nurminski, E., Pardalos, P. (eds) Discrete Optimization and Operations Research. DOOR 2016. Lecture Notes in Computer Science(), vol 9869. Springer, Cham. https://doi.org/10.1007/978-3-319-44914-2_36

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  • DOI: https://doi.org/10.1007/978-3-319-44914-2_36

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-44913-5

  • Online ISBN: 978-3-319-44914-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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