Article ID: | iaor20131207 |
Volume: | 55 |
Issue: | 2 |
Start Page Number: | 209 |
End Page Number: | 226 |
Publication Date: | Feb 2013 |
Journal: | Journal of Global Optimization |
Authors: | Li G, Jeyakumar V |
Keywords: | programming: quadratic |
In this paper we examine non‐convex quadratic optimization problems over a quadratic constraint under unknown but bounded interval perturbation of problem data in the constraint and develop criteria for characterizing robust (i.e. uncertainty‐immunized) global solutions of classes of non‐convex quadratic problems. Firstly, we derive robust solvability results for quadratic inequality systems under parameter uncertainty. Consequently, we obtain characterizations of robust solutions for uncertain homogeneous quadratic problems, including uncertain concave quadratic minimization problems and weighted least squares. Using homogenization, we also derive characterizations of robust solutions for non‐homogeneous quadratic problems.