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Abstract: In this paper, a global optimization algorithm is proposed for solving sum of generalized polynomial ratios problem (P) which arises in various practical problems. Due to its intrinsic difficulty, less work has been devoted to globally solve the problem (P). For such problems, we present a branch and bound algorithm. In this method, by utilizing exponent transformation and new three-level linear relaxation method, a sequence of linear relaxation programming of the initial nonconvex programming problem (P) are derived which are embedded in a branch and bound algorithm. The proposed method need not introduce new variables and constraints and it is convergent to the global minimum of prime problem by means of the subsequent solutions of a series of linear programming problems. Several numerical examples in the literatures are tested to demonstrate that the proposed algorithm can systematically solve these examples to find the approximate ϵ-global optimum. [Copyright &y& Elsevier]

Abstract: In this technical note, we give a short extension application for a deterministic global optimization algorithm proposed in [Y. Ji, K.-C. Zhang, S.-J. Qu, A deterministic global optimization algorithm, Applied Mathematics and Computation 185 (2007) 382–387]. Actually our result is slightly more general, since it does not impose any special sign restrictions on numerators and denominators of the ratios. The only assumption is that the denominators of the ratios are nonzero over the feasible region of the problem. For clarity we use the same notations for the different equivalent problems and the corresponding relaxation linear programming (RLP) as done in Ji et al. (2007). [Copyright &y& Elsevier]

Abstract: This paper presents a global optimization algorithm for a class of multiplicative programming with exponent under multiplicative constraints (MPE). By utilizing equivalent problem of MPE in the sense that they have the same optimal solution, tangential hypersurfaces and concave envelope approximations a linear relaxation of equivalent problem is received. Thus the initial nonconvex programming problem (MPE) is reduced to a sequence of linear programming problems through the successive refinement of a linear relaxation of feasible region of the objective function. The proposed algorithm is convergent to the globally optimal solution of MPE by means of the subsequent solutions of a series of linear programming problems. Numerical results indicate that the proposed algorithm is extremely robust and can be used successfully to solve global minimum of MPE on microcomputer. [Copyright &y& Elsevier]