M.Sc Student | Daureen Steinberg |
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Subject | Computation of Matrix Norms with Applications to Robust Optimization |

Department | Department of Industrial Engineering and Management |

Supervisor | Full Professor Nemirovski Arkadi |

The research is devoted to investigating the problem of
computing the norm ||*A*||_{E,F}=max||*Ax*||_{F}: *xєE,*||*x*||_{E}≤1of
linear mapping *x*→*Ax*, acting from a finite dimensional
normed space (*E,*|| ^{.} ||* _{E}*) to a finite
dimensional normed space (

1≤ *r *≤ 2 ≤ *p *≤ ∞,
is much less conservative in a wide range of values of *p,r *than the 2.29
factor suggested by Nestrov. Finally we develop a simple interpolation
technique allowing to extend the efficiently upper bound on ||*A*||_{p,r}
from its original domain to the entire range of *p *≥ 1, *r *≥
1 and we showed that the extended bound is tight within a factor depending on *p,n,r,m*
and never exceeding *O(*1)(max(*m,n)) ^{25/128}*. Our analysis
demonstrates that this factor does not exceed 9.48 for all