Optimizing the sum of linear fractional functions and applications
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Maximization of the Ratio of Two Convex Quadratic Functions over a Polytope
Computational Optimization and Applications
Solving the Sum-of-Ratios Problem by an Interior-Point Method
Journal of Global Optimization
A branch-and-bound algorithm for maximizing the sum of several linear ratios
Journal of Global Optimization
Using concave envelopes to globally solve the nonlinear sum of ratios problem
Journal of Global Optimization
Global optimization algorithm for the nonlinearsum of ratios problem
Journal of Optimization Theory and Applications
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
Multisubject learning for common spatial patterns in motor-imagery BCI
Computational Intelligence and Neuroscience - Special issue on Selected Papers from the 4th International Conference on Bioinspired Systems and Cognitive Signal Processing
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This article presents a simplicial branch and duality bound algorithm for globally solving the sum of convex-convex ratios problem with nonconvex feasible region. To our knowledge, little progress has been made for globally solving this problem so far. The algorithm uses a branch and bound scheme where the Lagrange duality theory is used to obtain the lower bounds. As a result, the lower-bounding subproblems during the algorithm search are all ordinary linear programs that can be solved very efficiently. It has been proved that the algorithm possesses global convergence. Finally, the numerical experiments are given to show the feasibility of the proposed algorithm.