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Computing exact solution to nonlinear integer programming: Convergent Lagrangian and objective level cut method

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Abstract

In this paper, we propose a convergent Lagrangian and objective level cut method for computing exact solution to two classes of nonlinear integer programming problems: separable nonlinear integer programming and polynomial zero-one programming. The method exposes an optimal solution to the convex hull of a revised perturbation function by successively reshaping or re-confining the perturbation function. The objective level cut is used to eliminate the duality gap and thus to guarantee the convergence of the Lagrangian method on a revised domain. Computational results are reported for a variety of nonlinear integer programming problems and demonstrate that the proposed method is promising in solving medium-size nonlinear integer programming problems.

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Authors and Affiliations

  1. Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, N. T., Hong Kong

    D. Li

  2. Department of Management Science and Engineering, International Business College, Qingdao University, Qingdao, 266071, China

    J. Wang

  3. Department of Management Science, School of Management, Fudan University, Shanghai, 200433, China

    X. L. Sun

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  1. D. Li
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  2. J. Wang
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  3. X. L. Sun
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Correspondence to D. Li.

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Li, D., Wang, J. & Sun, X.L. Computing exact solution to nonlinear integer programming: Convergent Lagrangian and objective level cut method. J Glob Optim 39, 127–154 (2007). https://doi.org/10.1007/s10898-006-9128-7

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  • DOI: https://doi.org/10.1007/s10898-006-9128-7

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