Since your problem includes inequality constraints,  the simple method I suggested doesn't
apply;  it only works for problems involving only linear equality constraints.

To use the method, you need to identify the nullspace of your constraint matrix, e.g., using
a singular value decomposition.  



On 6/17/07, fdu.xiaojf@gmail.com < fdu.xiaojf@gmail.com> wrote:
Hi Joachim,

Joachim Dahl wrote:
> If your function is too complicated to evaluate derivatives,  chances
> are that
> it's not convex.  But you're still going to need the first and second
> order derivatives
> for Newton's method...
>
> If you want to solve
>
> min.  f(x)
> s.t.    A*x = b
>
> you could first find a feasible point x0 satisfying A*x0 = b (e.g., the
> least-norm solution to A*x = b) and parametrize all feasible points as
>
> z = x0+ B*y
>
> where B spans the nullspace of A, i.e., A*B = 0.  Now you have an
> unconstrained
> problem
>
> min.  f( x0 + B*y )
>
> over the new variable y.
>

I still don't quite understand how to liminate linear equality
constraints.  Could you please point me to some web resources that
describe this method in detail? Or what key words I should use if I want
to google on the web?

Thanks.

Xiao Jianfeng
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