Global optimization for the sum of generalized polynomial fractional functions |
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Authors: | Shen Pei-Ping Yuan Gui-Xia |
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Institution: | (1) College of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, China |
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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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Keywords: | Global optimization Generalized polynomial Fractional function Generalized polynomial constraint Linear relaxation Branch and bound |
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