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MathGroup Archive 2004

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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.
Adjunct Professor, Dalhousie University
129 Glenforest Drive, Halifax, NS, Canada B3M 1J2
Telephone:      +1-(902)-443-5910
Fax:            +1-(902)-431-5100; +1-(902)-443-5910
E-mail: jdpinter at hfx.eastlink.ca
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.
>Sorry for being so unhelpful.
>
>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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