Robust solutions of quadratic optimization over single quadratic constraint under interval uncertainty

Robust solutions of quadratic optimization over single quadratic constraint under interval uncertainty

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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: ,
Keywords: programming: quadratic
Abstract:

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.

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