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This paper presents a global optimization algorithm for solving the signomial geometric programming (SGP) problem. In the algorithm, by the straight forward algebraic manipulation of terms and by utilizing a transformation of variables, the initial nonconvex programming problem (SGP) is first converted into an equivalent monotonic optimization problem and then is reduced to a sequence of linear programming problems, based on the linearizing technique. To improve the computational efficiency of the algorithm, two range reduction operations are combined in the branch and bound procedure. The proposed algorithm is convergent to the global minimum of the (SGP) by means of the subsequent solutions of a series of relaxation linear programming problems. And finally, the numerical results are reported to vindicate the feasibility and effectiveness of the proposed method.

This paper is concerned with an efficient global optimization algorithm for solving a kind of fractional program problem (P), whose objective and constraints functions are all defined as the sum of ratios generalized polynomial functions. The proposed algorithm is a combination of the branch-and-bound search and two reduction operations, based on an equivalent monotonic optimization problem of (P). The proposed reduction operations specially offer a possibility to cut away a large part of the currently investigated region in which the global optimal solution of (P) does not exist, which can be seen as an accelerating device for the solution algorithm of (P). Furthermore, numerical results show that the computational efficiency is improved by using these operations in the number of iterations and the overall execution time of the algorithm, compared with other methods. Additionally, the convergence of the algorithm is presented, and the computational issues that arise in implementing the algorithm are discussed. Preliminary indications are that the algorithm can be expected to provide a practical approach for solving problem (P) provided that the number of variables is not too large. [ABSTRACT FROM AUTHOR]