Abstract
In this paper, a branch and bound approach is proposed for global optimization problem (P) of the sum of generalized polynomial fractional functions under generalized polynomial constraints, which arises in various practical problems. Due to its intrinsic difficulty, less work has been devoted to globally solving this problem. By utilizing an equivalent problem and some linear underestimating approximations, a linear relaxation programming problem of the equivalent form is obtained. Consequently, the initial non-convex nonlinear problem (P) is reduced to a sequence of linear programming problems through successively refining the feasible region of linear relaxation problem. The proposed algorithm is convergent to the global minimum of the primal problem by means of the solutions to a series of linear programming problems. Numerical results show that the proposed algorithm is feasible and can successfully be used to solve the present problem (P).
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Pei-Ping, S., Gui-Xia, Y. Global optimization for the sum of generalized polynomial fractional functions. Math Meth Oper Res 65, 445–459 (2007). https://doi.org/10.1007/s00186-006-0130-0
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DOI: https://doi.org/10.1007/s00186-006-0130-0