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A Survey of Methods for Pure Nonlinear Integer Programming

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  • Mary W. Cooper

    (Southern Methodist University)

Abstract

The subject of this paper is a classification and discussion of algorithms for solution of nonlinear pure integer programming problems. The survey is organized by characterizing the mathematical form of the nonlinear optimization problems addressed by the various algorithms. If any method can be used without changes to solve mixed integer nonlinear programming problems that fact is mentioned in the description of the algorithm. However algorithms which must be applied only to mixed integer problems are not surveyed.

Suggested Citation

  • Mary W. Cooper, 1981. "A Survey of Methods for Pure Nonlinear Integer Programming," Management Science, INFORMS, vol. 27(3), pages 353-361, March.
    • Handle: RePEc:inm:ormnsc:v:27:y:1981:i:3:p:353-361
    DOI: 10.1287/mnsc.27.3.353
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    Cited by:

    1. D. Quadri & E. Soutif & P. Tolla, 2009. "Exact solution method to solve large scale integer quadratic multidimensional knapsack problems," Journal of Combinatorial Optimization, Springer, vol. 17(2), pages 157-167, February.
    2. Bretthauer, Kurt M. & Ross, Anthony & Shetty, Bala, 1999. "Nonlinear integer programming for optimal allocation in stratified sampling," European Journal of Operational Research, Elsevier, vol. 116(3), pages 667-680, August.
    3. Kurt M. Bretthauer & Bala Shetty & Siddhartha Syam, 2003. "A specially structured nonlinear integer resource allocation problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(7), pages 770-792, October.
    4. Sarathy, Rathindra & Shetty, Bala & Sen, Arun, 1997. "A constrained nonlinear 0-1 program for data allocation," European Journal of Operational Research, Elsevier, vol. 102(3), pages 626-647, November.
    5. Juan S. Borrero & Colin Gillen & Oleg A. Prokopyev, 2017. "Fractional 0–1 programming: applications and algorithms," Journal of Global Optimization, Springer, vol. 69(1), pages 255-282, September.
    6. Reiner Horst, 1990. "Deterministic methods in constrained global optimization: Some recent advances and new fields of application," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(4), pages 433-471, August.
    7. Yuji Nakagawa & Ross J. W. James & César Rego & Chanaka Edirisinghe, 2014. "Entropy-Based Optimization of Nonlinear Separable Discrete Decision Models," Management Science, INFORMS, vol. 60(3), pages 695-707, March.
    8. Yasemin Aksoy, 1990. "An interactive branch‐and‐bound algorithm for bicriterion nonconvex/mixed integer programming," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(3), pages 403-417, June.

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