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On a Finite Branch and Bound Algorithm for the Global Minimization of a Concave Power Law Over a Polytope

Author

Listed:
  • Vasilios I. Manousiouthakis

    (UCLA)

  • Neil Thomas

    (UCLA)

  • Ahmad M. Justanieah

    (King Abdul Aziz University)

Abstract

In this paper, a finite branch-and-bound algorithm is developed for the minimization of a concave power law over a polytope. Linear terms are also included in the objective function. Using the first order necessary conditions of optimality, the optimization problem is transformed into an equivalent problem consisting of a linear objective function, a set of linear constraints, a set of convex constraints, and a set of bilinear complementary constraints. The transformed problem is then solved using a finite branch-and-bound algorithm that solves two convex problems at each of its nodes. The method is illustrated by means of an example from the literature.

Suggested Citation

  • Vasilios I. Manousiouthakis & Neil Thomas & Ahmad M. Justanieah, 2011. "On a Finite Branch and Bound Algorithm for the Global Minimization of a Concave Power Law Over a Polytope," Journal of Optimization Theory and Applications, Springer, vol. 151(1), pages 121-134, October.
    • Handle: RePEc:spr:joptap:v:151:y:2011:i:1:d:10.1007_s10957-011-9863-x
    DOI: 10.1007/s10957-011-9863-x
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    References listed on IDEAS

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