Abstract
In this paper, we discuss complex convex quadratically constrained optimization with uncertain data. Using S-Lemma, we show that the robust counterpart of complex convex quadratically constrained optimization with ellipsoidal or intersection-of-two-ellipsoids uncertainty set leads to a complex semidefinite program. By exploring the approximate S-Lemma, we give a complex semidefinite program which approximates the NP-hard robust counterpart of complex convex quadratic optimization with intersection-of-ellipsoids uncertainty set.
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Huang, Z. H., Sun, D., Zhao, G. Y.: A smoothing Newton-type algorithm of stronger convergence for the quadratically constrained convex quadratic programming. Comput. Optim. Appl., 35, 199–237 (2006)
Xu, D., Ye, Y., Zhang, J.: Approximate the 2-catalog segmentation problem using semidefinite programming relaxation. Optimization Method and Software, 18, 705–719 (2003).
Xu, D., Zhang, S.: Approximation bounds for quadratic maximization with semidefinite programming relaxation. Science in China (Series A), 50, 1583–1596 (2007)
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Research supported by NSF of China (Grant No. 60773185, 10401038) and Program for Beijing Excellent Talents and NSF of China (Grant No. 10571134) and the Natural Science Foundation of Tianjin (Grant No. 07JCYBJC05200)
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Xu, D.C., Huang, Z.H. Robust solutions of uncertain complex-valued quadratically constrained programs. Acta. Math. Sin.-English Ser. 24, 1279–1290 (2008). https://doi.org/10.1007/s10114-008-5656-z
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DOI: https://doi.org/10.1007/s10114-008-5656-z