In this paper a deterministic method is proposed for the global optimization of mathematical programs that involve the sum of linear fractional and/or bilinear terms. Linear and nonlinear convex estimator functions are developed for the linear fractional and bilinear terms. Conditions under which these functions are nonredundant are established. It is shown that additional estimators can be obtained through projections of the feasible region that can also be incorporated in a convex nonlinear underestimator problem for predicting lower bounds for the global optimum. The proposed algorithm consists of a spatial branch and bound search for which several branching rules are discussed. Illustrative examples and computational results are presented to demonstrate the efficiency of the proposed algorithm.
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Quesada, I., Grossmann, I.E. A global optimization algorithm for linear fractional and bilinear programs. J Glob Optim 6, 39–76 (1995). https://doi.org/10.1007/BF01106605
- Nonconvex optimization
- bilinear programming
- fractional programming
- convex under estimators