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Regional division and reduction algorithm for minimizing the sum of linear fractional functions
1College of Mathematics and Information Science, Henan Normal University, Xinxiang, P.R. China.
Journal of Inequalities and Applications
|April 3, 2018
Summary
This study introduces a new algorithm for minimizing sums of linear fractional functions over polyhedra. The method efficiently narrows down the search space to find the global minimum.
Area of Science:
- Optimization Theory
- Mathematical Programming
- Operations Research
Background:
- Minimizing sums of linear fractional functions over polyhedra is a complex problem in mathematical optimization.
- Existing algorithms may face challenges with efficiency and convergence for certain problem classes.
Purpose of the Study:
- To develop a practicable regional division and cut algorithm for minimizing the sum of linear fractional functions over a polyhedron.
- To enhance the efficiency of global optimization by effectively reducing the search space.
Main Methods:
- The algorithm utilizes an equivalent problem (P) and introduces a generalized bisection operation.
- It incorporates deleting and reduction operations to prune regions where the global optimum of (P) cannot exist.
- Key computations involve solving a sequence of strictly monotonic univariate equations.
Main Results:
- The proposed algorithm demonstrates convergence to the global minimum.
- Numerical results confirm the feasibility and effectiveness of the developed method.
- The algorithm successfully cuts away large portions of the investigated region, improving efficiency.
Conclusions:
- The presented regional division and cut algorithm offers a viable approach for solving this class of optimization problems.
- The method's convergence and efficiency are supported by computational evidence.
- This work contributes a practical tool for the minimization of sums of linear fractional functions over polyhedra.
Keywords:
Fractional programmingGlobal optimizationRegional division and reductionSum of linear ratiosMore Related Videos
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