Title:
Generalized Fractional Programming with User Interaction

Authors:
S. I. Birbil
Erasmus Research Institute of Management
Erasmus University Rotterdam
Postbus 1738
3000 DR Rotterdam
The Netherlands
and 
J.B.G. Frenk
Econometric Institute
Erasmus University Rotterdam
Postbus 1738
3000 DR Rotterdam
The Netherlands
and 
Shuzhong Zhang
Department of Systems Engineering and Engineering Management
The Chinese University of Hong Kong
Shatin, Hong Kong

Abstract:
  The present paper proposes a new approach to solve generalized
  fractional programming problems with approximation. Capitalizing on
  two alternatives, we review the Dinkelbach-type methods and set
  forth the main difficulty in applying these methods.  In order to
  cope with this difficulty, we propose an approximation approach that
  can be controlled by a predetermined parameter. The proposed
  approach is promising particularly when it is acceptable to find an
  effective, but near-optimal value in an efficient manner. Once the
  approximation parameter is fixed, our analysis shows how good is the
  value found by the approximation. In addition, we present several
  observations that may be suitable for improving the performance of
  the proposed approach.  Finally, we support our discussion through
  numerical experiments.