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

Authors:
D. Li;J. Wang;X. L. Sun
Affiliations:
Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, N. T., Hong Kong;Department of Management Science and Engineering, International Business College, Qingdao University, Qingdao, China 266071;Department of Management Science, School of Management, Fudan University, Shanghai, China 200433
Venue:
Journal of Global Optimization
Year:
2007

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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.