optim suggestion

[Gianluca Antonelli]

Hi,

I would like to ask for advice to use the "optim" command for the
following optimization problem.

I need to find x that minimize

PHI*x = b

given some bound constraints on x, all its values are positive and
less than 1, some are null by definition.

The matrix PHI containts all 1 and zero except for the last row that
exhibits numbers of magnitude 1000

The vector b contains all numbers of magnitude 1 in correspondance to
the 1-0 of PHI except for the last row that contains a number of
magnitude 100000

I use the following code:

--------------
[f_opt, m_sol] = optim(costf,'b',m_min,m_max,.4*ones(m*n,1),imp=2);

function [f, g, ind] = costf(x, ind)

   alpha = 0*1e-10;
   W = eye(n*m,n*m);
   Q = eye(m+1,m+1);
   Q(m+1,m+1) = 1e-6;
   f = (PHI*x - b)'*Q*(PHI*x - b) + alpha*x'*W*x;
   g = 2*x'*(PHI'*Q*PHI+alpha*W)-2*b'*Q*PHI;

endfunction
---------

but I always receive error messages such as "linear search fail" or
similar.

Two questions:

a) any suggestion on the syntax/algorithm/etc.

b) the fact that some of the unknown are fixed with lower bound equal
to upper bound is a problem for the code?

thanks in advance,
g.