Re: a question regarding optimization theory
- From: Hans Mittelmann <mittelmann@xxxxxxx>
- Date: Sun, 17 Feb 2008 07:46:32 -0800 (PST)
On Feb 17, 5:40 am, zingas <shammashah...@xxxxxxxxx> wrote:
MY problem is actually
i have a matrix
a1*x1 +a2*x2 +a3*x3 +a4*x4 +a5*x5 +a6*x6=0
b1*x1 +b2*x2 +b3*x3 +b4*x4 +b5*x5 +b6*x6=0
c1*x1 +c2*x2 +c3*x3 +c4*x4 +c5*x5 +c6*x6=0
where a1..a6 and b1....b6, c1...c6 are all known and x1 x2...x6 are
all unknowns .....my problems is more like an undetermined linear
equations but i have some constraints to the solutions of the
x1......x6
1)all the x1 ....x6 must be positive and non zero
2)x1^2 +x2^2........+x6^2=6
i know that it is going to be solved by non linear programming ..i
tried like this
using reduced gradient method
minimize x1^2 +x2^2........+x6^2-6
subject to
a1*x1 +a2*x2 +a3*x3 +a4*x4 +a5*x5 +a6*x6
b1*x1 +b2*x2 +b3*x3 +b4*x4 +b5*x5 +b6*x6
c1*x1 +c2*x2 +c3*x3 +c4*x4 +c5*x5 +c6*x6
x1,x2,x3,x4,x5,x6 =>0
can anybody tell me i am doing the right thing and secondly if i am
doing right i need a type of algorithm in which the constraint
x1,x2,x3,x4,x5,x6 =>0 does not include a zero term that is all of the
solutions must be non zero but reduced gradient oesnt gaurantee me
that ....which algorithm should i try
thanx for your patience
Hi,
phrase it as pure feasibility problem (no objective) and in AMPL and
submit to one of the suitable NEOS solvers, for example, to
http://neos.mcs.anl.gov/neos/solvers/go:icos/AMPL.html
Positivity probably needs to be enforced by requiring x_i >= eps. Look
at the sample submission problems (click on name) and
phrase accordingly. Let me know if it does not work.
HM
.
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