A simplicial branch and duality bound algorithm for the sum of convex-convex ratios problem
The proposed algorithm computes the lower bounds required during the branch and bound search by solving linear programming problems. These problems are derived by using Lagrangian weak duality theorem of nonlinear programming. The feasibility and efficiency of the proposed algorithm is shown by computational results for a set of randomly generated test problems. It is pointed out that the algorithm applies to a broad class of convex-convex ratio problems, and furthermore, the primary work of the algorithm involves the solution of ordinary linear programming problems that do not grow in size from iteration to iteration.
scientific article; zbMATH DE number 5370025