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A Newton’s method for the continuous quadratic knapsack problem

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Abstract

We introduce a new efficient method to solve the continuous quadratic knapsack problem. This is a highly structured quadratic program that appears in different contexts. The method converges after \(O(n)\) iterations with overall arithmetic complexity \(O(n^2)\). Numerical experiments show that in practice the method converges in a small number of iterations with overall linear complexity, and is faster than the state-of-the-art algorithms based on median finding, variable fixing, and secant techniques.

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Authors and Affiliations

  1. Departamento de Ingeniería Industrial, Universidad de Chile, Santiago, Chile

    Roberto Cominetti

  2. Computer Science Department, University of São Paulo, São Paulo, Brazil

    Walter F. Mascarenhas

  3. Applied Mathematics Department, University of Campinas, Campinas, Brazil

    Paulo J. S. Silva

Authors
  1. Roberto Cominetti
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  2. Walter F. Mascarenhas
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  3. Paulo J. S. Silva
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Corresponding author

Correspondence to Paulo J. S. Silva.

Additional information

This work was supported by Fondecyt 1100046 and Nucleo Milenio Información y Coordinación en Redes ICM/FIC P10-024F, PRONEX-Optimization (PRONEX-CNPq/FAPERJ E-26/171.510/2006-APQ1), CNPq (Grant 305740/2010-5), and FAPESP (Grant 2012/20339-0).

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Cominetti, R., Mascarenhas, W.F. & Silva, P.J.S. A Newton’s method for the continuous quadratic knapsack problem. Math. Prog. Comp. 6, 151–169 (2014). https://doi.org/10.1007/s12532-014-0066-y

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  • DOI: https://doi.org/10.1007/s12532-014-0066-y

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