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.
Original language | English |
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Pages (from-to) | 337-353 |
Number of pages | 17 |
Journal | Journal of Global Optimization |
Volume | 45 |
Issue number | 3 |
DOIs | |
Publication status | Published - 2009 Nov |
All Science Journal Classification (ASJC) codes
- Computer Science Applications
- Management Science and Operations Research
- Control and Optimization
- Applied Mathematics