A bisection algorithm for linear-fractional programming is a method used to solve optimization problems where the objective function is a linear combination of variables and the constraints are in the form of linear-fractional inequalities. It involves repeatedly dividing the feasible region in half and checking which half contains the optimal solution until the solution is found.
The bisection algorithm works by first finding an initial feasible solution to the problem. Then, it checks the midpoint of the feasible region and determines which half of the region contains the optimal solution. This process is repeated until the optimal solution is found within a desired level of accuracy.
The bisection algorithm is a simple and efficient method for solving linear-fractional programming problems. It guarantees convergence to the optimal solution and does not require any derivatives of the objective function or constraints.
One limitation of the bisection algorithm is that it can be computationally expensive for large-scale problems. It also may not be suitable for problems with non-linear objective functions or constraints.
The bisection algorithm is considered a basic and reliable method for solving linear-fractional programming problems. However, it may not be as efficient as other methods such as the simplex method or interior-point methods for larger problems. It also has the advantage of not requiring any derivative information.