Re: How to solve a nonlinear non-differentiable equation in n-dimension?

From: Fan Yang (yang_at_cae.wisc.edu)
Date: 09/14/04 

Date: Tue, 14 Sep 2004 00:20:26 -0500

Dear Erwin,

Thank you very much for your reply.

Could you explain a little more in detail about what you
said using a dummy obj? What can be the dummy objective
function? Btw, do you have any reference of using smooth
apporixmations for max(z,0), such as any book or paper?
Can Gams solve the approximations very efficiently? If so,
what kind of module should we use in Gams?

Thanks agian,

Fan

"Erwin Kalvelagen" <erwin@gams.com> wrote in message
news:pan.2004.09.14.03.25.07.421293@gams.com...
>
> I think this is like:
> find x such that f(x)<=0
> May be an NLP solver using a dummy obj can handle
> this.
>
> Note also that there exist smooth approximations for
> max(z,0), such as:
>
> z + (1/a) log(1+exp(-a*z)) for some a>0, e.g. a=10
>
> or
>
> [sqrt(z^2 + a^2) + z]/2 for some a>0, e.g. a=0.0001
>
> Erwin
>
> ----------------------------------------------------------------
> Erwin Kalvelagen
> GAMS Development Corp., http://www.gams.com
> erwin@gams.com, http://www.gams.com/~erwin
> ----------------------------------------------------------------
>
>
> On Mon, 13 Sep 2004 21:15:26 -0500, Fan Yang wrote:
>
> > Dear all,
> >
> > I am facing to solve a nonlinear non-differentiable equation
> > in n-dimension.
> >
> > The problem is to solve
> > max(f(x), 0) = 0, x belongs to R(n).
> > where f is a continuously differentiable map from R(n) to R(n).
> >
> > Seems the family of Newton methods will fail. Will bisection
> > method work in this case? I only know how to use bisection
> > method in 1-dimension, not the higher dimension. Or there
> > exists some other more efficient methods?
> >
> > Thanks a lot,
> >
> > Fan
>