Effectiveness of a geometric programming algorithm for optimization of machining economics models
Computers and Operations Research
Recent developments and trends in global optimization
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. IV: optimization and nonlinear equations
Monotonic Optimization: Problems and Solution Approaches
SIAM Journal on Optimization
Solving the Sum-of-Ratios Problem by an Interior-Point Method
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
Optimization of Polynomial Fractional Functions
Journal of Global Optimization
An Improved Interval Global Optimization Algorithm Using Higher-order Inclusion Function Forms
Journal of Global Optimization
Robust Solution of Nonconvex Global Optimization Problems
Journal of Global Optimization
A robust algorithm for quadratic optimization under quadratic constraints
Journal of Global Optimization
A robust algorithm for generalized geometric programming
Journal of Global Optimization
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In this paper, a new deterministic global optimization algorithm is proposed for solving a fractional programming problem whose objective and constraint functions are all defined as the sum of generalized polynomial ratios, which arises in various practical problems. Due to its intrinsic difficulty, less work has been devoted to globally solving this problem. The proposed algorithm is based on reformulating the problem as a monotonic optimization problem, and it turns out that the optimal solution which is provided by the algorithm is adequately guaranteed to be feasible and to be close to the actual optimal solution. Convergence of the algorithm is shown and numerical examples are given to illustrate the feasibility and efficiency of the present algorithm.