Global optimization for a class of fractional programming problems

Global optimization for a class of fractional programming problems

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Article ID: iaor200970814
Country: Netherlands
Volume: 45
Issue: 3
Start Page Number: 337
End Page Number: 353
Publication Date: Nov 2009
Journal: Journal of Global Optimization
Authors: , , ,
Keywords: duality
Abstract:

This paper presents a canonical dual approach to minimizing the sum of a quadratic function and the ratio of two quadratic functions, which is a type of non-convex optimization problem subject to an elliptic constraint. We first relax the fractional structure by introducing a family of parametric subproblems. Under proper conditions on the ‘problem-defining’ matrices associated with the three quadratic functions, we show that the canonical dual of each subproblem becomes a one-dimensional concave maximization problem that exhibits no duality gap. Since the infimum of the optima of the parameterized subproblems leads to a solution to the original problem, we then derive some optimality conditions and existence conditions for finding a global minimizer of the original problem. Some numerical results using the quasi-Newton and line search methods are presented to illustrate our approach.

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