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International Conference on Discrete Optimization and Operations Research

DOOR 2016: Discrete Optimization and Operations Research pp 430–440Cite as

Multiple Cuts in Separating Plane Algorithms

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

Abstract

This paper presents an extended version of the separation plane algorithm for subgradient-based finite-dimensional nondifferentiable convex optimization. The extension introduces additional cuts for epigraph of the conjugate of objective function which improve the convergence of the algorithm. The case of affine cuts is considered in more details and it is shown that it requires solution of an auxiliary convex subproblem the dimensionality of which depends on the number of additional cuts and can be kept arbitrary low. Therefore algorithm can make use of the efficient algorithms of low-dimensional nondifferentiable convex optimization which overcome known computational complexity bounds for the general case.

E. Nurminski—This work is supported by RFBR grant 13-07-1210.

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Author information

Authors and Affiliations

  1. School of Natural Sciences, Far Eastern Federal University, Ajax Street, Vladivostok, Russky Island, Russia

    Evgeni Nurminski

Authors
  1. Evgeni Nurminski
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Correspondence to Evgeni Nurminski .

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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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Nurminski, E. (2016). Multiple Cuts in Separating Plane Algorithms. 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_34

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  • DOI: https://doi.org/10.1007/978-3-319-44914-2_34

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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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