Solving a very strange minimization problem with Octave

[Topi, Corrado]

Dear Octave-ians,

I have to solve the following problem:

min || D_ij - SUM p | SUM k A_pk Q_ij| || (1)

or alternatively

min (SUM_ij (D_ij - SUM p | SUM k A_pk Q_ij|)^2) (2)

where I have to find the values of the Apk>=0 which minimize the 
distance (1) or alternatively the residual sum of square (2).

The problem is the || aroud the second SUM.

Is that feasible with Octave?

All the D_ij, Q_ij are real numbers with

0 <= D_ij <= 1
D_ii =0
D_ij=D_ji

for each i,j belonging to {1 .... n}

I have been breaking my head on it for several days, read tons of 
documentation, and papers, and now I am going to ask as last resort ....

Regards
--
Corrado Topi

Area 18,Department of Biology
University of York, York, YO10 5YW, UK
Phone: + 44 (0) 1904 328645, E-mail: address@hidden