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Solving a class of generalized fractional programming problems using the feasibility of linear programs.

Peiping Shen1, Tongli Zhang1, Chunfeng Wang1

  • 1College of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007 P.R. China.

Journal of Inequalities and Applications
|July 7, 2017
PubMed
Summary

This study introduces a novel approximation algorithm for generalized fractional programming problems. The method efficiently solves these problems without requiring specific function properties, offering a new computational approach.

Keywords:
approximation algorithmcomputational complexitygeneralized fractional programmingglobal optimization

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Area of Science:

  • Optimization Theory
  • Computational Mathematics
  • Operations Research

Background:

  • Generalized fractional programming problems involve complex objective functions.
  • Existing algorithms often require restrictive assumptions like quasi-concavity.

Purpose of the Study:

  • To present a new approximation algorithm for solving generalized fractional programming problems.
  • To develop a method that does not rely on restrictive assumptions on the objective function.

Main Methods:

  • Solving an equivalent optimization problem (Q) using a nonuniform grid exploration.
  • Checking the feasibility of linear programs at grid points.

Main Results:

  • The algorithm is a fully polynomial time approximation scheme for fixed ratio terms.
  • It overcomes limitations of existing methods by not assuming quasi-concavity or low-rank.

Conclusions:

  • The proposed algorithm is feasible and effective for generalized fractional programming.
  • This work provides a more general approach to solving these optimization problems.