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In this paper, we study the problem of maximizing the sum of a concave–convex quadratic fractional function on a non-empty, bounded, convex quadratic feasible set, which is called the problem (QCQFP). By using a conventional semidefinite program (SDP) relaxation, QCQFP is reformulated as a class of linear fractional programming problems over the cone of positive semidefinite matrices, which we refer to these problems as SDFP. After expatiating the properties of SDFP, we transform SDFP into its equivalent problem (ESDFP) whose non-convexity is mainly reflected in the newly added nonlinear equality constraints. By relaxing these nonlinear equality constraints into linear constraints, a special SDP relaxation is generated for ESDFP. Based on these results, an effective branch-and-bound algorithm is designed, and its theoretical convergence and worst-case complexity are proved. Numerical experiments demonstrate that the proposed algorithm is effective and feasible. [ABSTRACT FROM AUTHOR]

In this study, we investigate a class of linear multiplicative programs with positive exponents. By introducing p additional variables, the original problem is reformulated into an equivalent problem (EP) within the output space. Subsequently, a novel global optimization algorithm is introduced to tackle EP. The algorithm primarily leverages two key techniques. One is the outer approximation technique, which tightens the relaxed feasible region of EP and improves the upper bound by carefully examining suitable feasible points. The other is the branch and bound technique to guarantee the global optimality of the solution. Numerical results confirm the effectiveness and practicality of the proposed algorithm, thereby underscoring its potential for real-world applications. [ABSTRACT FROM AUTHOR]