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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The authors are grateful to the referee and the editors for their valuable comments and constructive suggestions which have contributed to the final preparation of the paper. Research was partially supported by a grant from the Australian Research Council.
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Jeyakumar, V., Li, G.Y. Robust solutions of quadratic optimization over single quadratic constraint under interval uncertainty. J Glob Optim 55, 209–226 (2013). https://doi.org/10.1007/s10898-012-9857-8
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DOI: https://doi.org/10.1007/s10898-012-9857-8
Keywords
- Non-convex quadratic programming under uncertainty
- Robust optimization
- Single quadratic constraint
- Robust solutions
- Global optimality conditions