Minimizing matrix norm

I have the following problem: given n x n symmetric real matrices

A, F1, ..., Fm,

I want to minimize the matrix 2-norm of

||A - \sum_i c_i F_i||, c_i \in R

(i.e. the norm of A as an operator from R^n to R^n with the usual
Euclidean norms).

I know how to use SDP to minimize the maximum eigenvalue of

A - \sum_i c_i F_i.

What I've been doing is doubling the dimension, replacing A by the block
matrix

( A 0 )
( 0 -A )

and the Fi by

( Fi 0 )
( 0 -Fi)

and minimizing the maximum eigenvalue of the new problem. (It isn't
quite as bad as it sounds, because SDP solvers can usually take
advantage of block structure like this.)

This works, but am I missing something? Is there a more direct way?

--
Ron Bruck
.

Relevant Pages

  • Re: Minimizing matrix norm
    ... It is a matrix norm but just ... and minimizing the maximum eigenvalue of the new problem. ... quite as bad as it sounds, because SDP solvers can usually take ... advantage of block structure like this.) ...
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  • Re: Minimizing matrix norm
    ... the solutions are rational (as is the square of the Frobenius ... harder] operator norm. ... and minimizing the maximum eigenvalue of the new problem. ... advantage of block structure like this.) ...
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