Global optimization for a class of fractional programming problems
The authors present a canonical dual approach to minimizing the sum of a quadratic function and the ratio of two quadratic functions subject to an elliptic constraint. First, they parameterize the original problem into a family of subprograms, in which each subproblem is a (possibly non-convex) quadratic program subject to one quadratic constraint. Then, it is shown that the infimum of the optima of the parameterized subproblems provides a solution to the original problem. For each subproblem a canonical dual subproblem is derived. For these pairs the authors provide some sufficient conditions to establish both the weak and strong duality theorems. The paper develops some existence conditions under which a global optimizer of the original problem can be identified by solving the corresponding canonical dual problems. Some numerical results using the quasi-Newton and line search methods are presented.
scientific article; zbMATH DE number 5633313
scientific article