Optimization of objective function that's the product of unitary matrices

[bastpg]

Hi,
I work in NRM and need for some reason to optimize an objective function of the form ||M-M_target||^2 where M is the product of a large number (>100) 2D unitary complex matrices (Qi) and a vector (A), i.e. M=Q1*Q2*...*QN*A, and M_target is a constant complex vector. I can do it directly, like people have done so far, but the problem has so much structure to it that it seems something smarter could be done. Note that this optimization should be fast, so reducing computation time even a little bit (>10%) could be a big deal. Let me know if the pb seems familiar and you have some ideas about it...
Thanks,
Bastien

 

[fresh_42]

I do not see shortcuts, as your M_target and A have nothing in common. You could at best use a faster algorithm for matrix multiplication, in this case the Strassen algorithm should save some time.

 

[RPinPA]

What is constant and what is a variable here?

 

[WWGD]

Only thing I can think of is, since squaring is monotonic for non-negatives, just seek to maximize ||M-M_target|| without concern for the square if you want to maximize or minimize difference if you wish to minimize the full expression.