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A New Global Optimization Algorithm for Solving a Class of Nonconvex Programming Problems

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  • Xue-Gang Zhou
  • Bing-Yuan Cao

Abstract

A new two-part parametric linearization technique is proposed globally to a class of nonconvex programming problems (NPP). Firstly, a two-part parametric linearization method is adopted to construct the underestimator of objective and constraint functions, by utilizing a transformation and a parametric linear upper bounding function (LUBF) and a linear lower bounding function (LLBF) of a natural logarithm function and an exponential function with e as the base, respectively. Then, a sequence of relaxation lower linear programming problems, which are embedded in a branch-and-bound algorithm, are derived in an initial nonconvex programming problem. The proposed algorithm is converged to global optimal solution by means of a subsequent solution to a series of linear programming problems. Finally, some examples are given to illustrate the feasibility of the presented algorithm.

Suggested Citation

  • Xue-Gang Zhou & Bing-Yuan Cao, 2014. "A New Global Optimization Algorithm for Solving a Class of Nonconvex Programming Problems," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-10, February.
    • Handle: RePEc:hin:jnljam:697321
    DOI: 10.1155/2014/697321
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