Re: Re: System of NonLinear Inequalities

```Colleagues,

systems of nonlinear equations and inequalities - under general analytical
conditions - can be transformed into global optimization problems that can
be solved numerically. (See e.g. my book 'Global Optimization in Action',
Ch. 4.1.) Of course, such systems may have no solution, infinitely many
solns, and 'anything in between'.

If you are interested in a single particular soln, then try to express the
quality of that soln by an 'objective function' and then you can solve a
std math programming (optimization) problem. For example, you may search
for the soln with minimal least squares error in an inconsistent system, or
you may like to find the soln that is closest to the origin, etc.

(The MathOptimizer Professional User Guide includes an example with
multiple solutions to a system of nonlinear equations, and how to handle
them numerically.)

Regards,
Janos Pinter
_________________________________________________

Janos D. Pinter, PhD, DSc
President & Research Scientist, PCS Inc.
129 Glenforest Drive, Halifax, NS, Canada B3M 1J2
Telephone:      +1-(902)-443-5910
Fax:            +1-(902)-431-5100; +1-(902)-443-5910
Web:            www.dal.ca/~jdpinter
www.pinterconsulting.com

At 08:19 AM 6/5/2004, Andrzej Kozlowski wrote:
>First of all, your inequalities are not written using Mathematica
>syntax (you can't use square brackets in this way). But looking at them
>I see it does not matter whether you use proper syntax or not: no
>computer program will ever solve a system of inequalites involving
>someting like x^(2/(2 - x)). Your only chance is a human brain and some
>fantastic stroke of luck.
>
>Andrzej
>
>On 4 Jun 2004, at 17:49, maurizio lisciandra wrote:
>
> > Dear Friends,
> >
> > I tried to solve the following system of nonlinear inequalities with
> > Mathematica 5.0:
> >
> > F < (1/2)*[a^(x/(2 - x))]*[x^(2/(2 - x))] &&
> > (2*a*B)^(x/2) + F - B > (2*a*F)^(x/2) &&
> > F > B > 0 &&
> > 0 <= a <= 1 &&
> > 0 < x < 2.
> >
> > I tried with Reduce, SolveInequality, SemiAlgebraicComponent,
> > FindInstance,
> > but all these function do not solve it. I tried to substitute x for
> > some
> > fixed value, but again I cannot solve it. The only value that I can
> > substitute for x is 1, and in this case the solution is an empty
> > space. I
> > may be happy if I find a value that solves the system, although I
> > really
> > need for which inetervals in the variable this system is not an empty
> > space.
> >
> > Hope some nice Mathematica expert can help me.
> >
> > Cheers,
> >
> > Maurizio Lisciandra
> > Trinity College
> > Cambridge (UK)
> >
> > _________________________________________________________________
> > Ricerche online più semplici e veloci con MSN Toolbar!
> > http://toolbar.msn.it/
> >
> >

```

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