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Global optimization of generalized geometric programming. (English) Zbl 1066.90096
Summary: In this paper a deterministic global optimization algorithm is proposed for locatingthe global minimum of the generalized geometric programming (GGP) problem. By utilizing an exponential variable transformation and some other techniques the initial nonconvex problem (GGP) is reduced to a typical reverse convex programming (RCP). Then a linear relaxation of problem (RCP) is obtained based on the famous arithmetic-geometric mean inequality and the linear upper bound of the reverse constraints inside some hyperrectangle region. The proposed branch and bound algorithm is convergent to the global minimum through the successive refinement of the linear relaxation of the feasible region of the objective function and the solutions of a series of linear optimization problems. And finally the numerical experiment is given to illustrate the feasibility and the robust stability of the present algorithm.

90C26Nonconvex programming, global optimization
90C57Polyhedral combinatorics, branch-and-bound, branch-and-cut
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