A spatial branch-reduction-bound algorithm for solving generalized linear fractional problems globally

In various engineering applications, the generalized linear fractional problem (GLFP) is an essential model that has many challenges in both theoretical and practical aspects. Therefore, the main work of this paper is to design an effective spatial algorithm for solving the GLFP efficiently. We start with equivalently converting the GLFP into an equivalent problem (EP) by transforming each fractional equation into one new variable. Next, applying the second-order cone relaxation to the constraint functions and executing a double-layer relaxation on the objective function of the EP, the second-order cone relaxed problem is constructed to underestimate the EP. Then, integrating some region reduction methods, we implement a spatial branch reduction-bound algorithm. Furthermore, we verified the convergence of the proposed algorithm. Equally important, the maximum iterations of the proposed algorithm in the worst scenario are evaluated by the complexity analysis of the proposed algorithm. Finally, by comparing some algorithms in the current literature, numerical results confirm the feasibility, robustness, and efficiency of the proposed algorithm.