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The Constrained Knapsack Problem: Models and the Polyhedral-Ellipsoid Method

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Mathematical Optimization Theory and Operations Research: Recent Trends (MOTOR 2021)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1476))

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Abstract

The paper focuses on studying a class KCFG of a Constrained Knapsack Problem (CKP), where conflict and forcing constraints are present. Four KCFG-formulations as quadratically constrained programs are introduced that utilize geometric properties of a feasible domain such as inscribability in an ellipsoid and coverability by two parallel planes. The new models are applied in deriving new upper bounds that can be effectively found by semi-definite programming and the r-algorithm. Another introduced application area is the Polyhedral-ellipsoid method (PEM) for linear optimization on two-level sets in a polytope \(P'\) (\(P'\)-2LSs) illustrated by a numerical example. Besides KCFG, the new modelling and solution approaches can be applied to any CKP reducible to a polynomial number of CKPs on \(P'\)-2LSs.

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Author information

Authors and Affiliations

  1. National Aerospace University “Kharkiv Aviation Institute”, 17 Chkalova Street, 61070, Kharkiv, Ukraine

    Oksana Pichugina

  2. University of Lodz, 3 Uniwersytecka Street, 90-137, Lodz, Poland

    Liudmyla Koliechkina

Authors
  1. Oksana Pichugina
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  2. Liudmyla Koliechkina
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Corresponding author

Correspondence to Oksana Pichugina .

Editor information

Editors and Affiliations

  1. Matrosov Institute for System Dynamics and Control Theory SB RAS, Irkutsk, Russia

    Alexander Strekalovsky

  2. Sobolev Institute of Mathematics SB RAS, Novosibirsk, Russia

    Yury Kochetov

  3. Matrosov Institute for System Dynamics and Control Theory SB RAS, Irkutsk, Russia

    Tatiana Gruzdeva

  4. Matrosov Institute for System Dynamics and Control Theory SB RAS, Irkutsk, Russia

    Andrei Orlov

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Pichugina, O., Koliechkina, L. (2021). The Constrained Knapsack Problem: Models and the Polyhedral-Ellipsoid Method. In: Strekalovsky, A., Kochetov, Y., Gruzdeva, T., Orlov, A. (eds) Mathematical Optimization Theory and Operations Research: Recent Trends. MOTOR 2021. Communications in Computer and Information Science, vol 1476. Springer, Cham. https://doi.org/10.1007/978-3-030-86433-0_16

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  • DOI: https://doi.org/10.1007/978-3-030-86433-0_16

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  • Online ISBN: 978-3-030-86433-0

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