Sums of random symmetric matrices and quadratic optimization under orthogonality constraints

@article{Nemirovski2007SumsOR,
  title={Sums of random symmetric matrices and quadratic optimization under orthogonality constraints},
  author={Arkadi Nemirovski},
  journal={Math. Program.},
  year={2007},
  volume={109},
  pages={283-317}
}
Let Bi be deterministic real symmetric m × m matrices, and ξi be independent random scalars with zero mean and “of order of one” (e.g., ξi ∼ N (0, 1)). We are interested to know under what conditions “typical norm” of the random matrix SN = ∑Ni=1 ξiBi is of order of 1. An evident necessary condition is E{SN} O(1)I, which, essentially, translates to ∑N i=1 Bi I; a natural conjecture is that the latter condition is sufficient as well. In the paper, we prove a relaxed version of this conjecture… CONTINUE READING
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