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.
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