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Global Optimization of Nonconvex Polynomial Programming Problems Having Rational Exponents

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Abstract

This paper considers the solution of nonconvex polynomial programming problems that arise in various engineering design, network distribution, and location-allocation contexts. These problems generally have nonconvex polynomial objective functions and constraints, involving terms of mixed-sign coefficients (as in signomial geometric programs) that have rational exponents on variables. For such problems, we develop an extension of the Reformulation-Linearization Technique (RLT) to generate linear programming relaxations that are embedded within a branch-and-bound algorithm. Suitable branching or partitioning strategies are designed for which convergence to a global optimal solution is established. The procedure is illustrated using a numerical example, and several possible extensions and algorithmic enhancements are discussed.

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Authors and Affiliations

  1. Department of Industrial and Systems Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA, 24061-0118, U.S.A.

    Hanif D. Sherali

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  1. Hanif D. Sherali
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Sherali, H.D. Global Optimization of Nonconvex Polynomial Programming Problems Having Rational Exponents. Journal of Global Optimization 12, 267–283 (1998). https://doi.org/10.1023/A:1008249414776

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