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A deterministic global optimization algorithm for generalized geometric programming. (English) Zbl 1105.65335
Summary: A deterministic global optimization algorithm is proposed for generalized geometric programming (GGP). By utilizing some transformations, the initial non-convex problem is reduced to a reverse convex programming (RCP), where the objective function and constraint functions are convex. Then a linear relaxation of the problem (RCP) is obtained based on the linear lower bounding functions of the convex constraint functions and the linear upper bounding functions of the reverse convex constraint functions inside some hyperrectangle region. A cutting-plane method is proposed to add some effective linear constraints to the linear relaxation programming based on the famous arithmetic-geometric mean inequality, then derive a tighter linear relaxation programming. The proposed global optimization algorithm which connects the branch and bound method with the cutting-plane method successfully 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 relaxation problems. Finally a numerical experiment is given to illustrate the feasibility and the robust stability of the present algorithm.

MSC:
65K05Mathematical programming (numerical methods)
90C26Nonconvex programming, global optimization
90C57Polyhedral combinatorics, branch-and-bound, branch-and-cut
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References:
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