[SciPy-user] lagrange multipliers in python

Joachim Dahl dahl.joachim@gmail....
Sun Jun 17 11:19:22 CDT 2007


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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