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This article presents and validates a new branch-and-bound algorithm for effectively solving the generalized polynomial problem (GPP). In this algorithm, a new affine relaxed technique is derived for establishing the relaxed linear programs problem of the GPP. In addition, some box reducing manipulations are employed to improve the speed of branch-and-bound search of the algorithm. Combining the relaxed linear programs problem with the box reducing manipulations, a new branch-and-bound algorithm is constructed. Some numerical examples are solved to verify the potential practical and computing advantages of the algorithm. At last, several engineering design problems are solved to validate the usefulness of the algorithm. [ABSTRACT FROM AUTHOR]

This paper presents a deterministic global optimization algorithm for solving minimax linear fractional programming (MLFP). In this algorithm, a new linearization technique is proposed, which uses more information of the objective function of the (MLFP) than other techniques. By utilizing this new linearization technique, the initial nonconvex programming problem (MLFP) is reduced to a sequence of linear relaxation programming (LRP) problems, which can provide reliable lower bound of the optimal value. The proposed algorithm is convergent to the global minimum of the (MLFP) through the successive refinement of the feasible region and solutions of a series of the (LRP). Compared with the known algorithms, numerical results show that the proposed algorithm is robust and effective. [ABSTRACT FROM PUBLISHER]