Global solutions to fractional programming problem with ratio of nonconvex functions

This paper presents a canonical dual approach for minimizing a sum of quadratic function and a ratio of nonconvex functions in Rⁿ. By introducing a parameter, the problem is first equivalently reformed as a nonconvex polynomial minimization with elliptic constraint. It is proved that under certain conditions, the canonical dual is a concave maximization problem in R² that exhibits no duality gap. Therefore, the global optimal solution of the primal problem can be obtained by solving the canonical dual problem.This paper was partially supported by a grant (AFOSR FA9550–10-1–0487) from the US Air Force Office of Scientific Research. Dr. Ning Ruan was supported by a funding from the Australian Government under the Collaborative Research Networks (CRN) program

A fractional programming approach for choice-based network revenue management

Choice-based revenue management -- Linear fractional programming -- General Form -- Linear fractional programming -- Single ratio -- Linear fractional programming -- Sum of several ratios -- Problem description and solution approaches -- Choice-based deterministic linear programming model -- Using column generation to solve the CDLP model -- Solution approaches for the column generation subproblem -- Numerical examples and evaluation of solution approaches -- A small airline network -- Thalys railroads example