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Re: solving set of inequalities
From: |
John W. Eaton |
Subject: |
Re: solving set of inequalities |
Date: |
Mon, 25 Jan 2010 13:31:49 -0500 |
On 25-Jan-2010, Petr Korviny wrote:
| As I mentioned above,
Above? Your new text appeared as the first thing in the message I
received, and there was nothing above it.
I need to find out solution of set of linear inequalities
| (to get values of variables x1,x2,x3,...) or to get an information of
| nonexistence any such solution.
|
| At this picture:
| http://suzelly.opf.slu.cz/~korviny/zzz/octave/excel_solver.png
| you can see utilization of Excel's Solver add-in I used to get solution of
| viewed set. "alpha" variable is always set to a number <0;1>, so set of
| inequalities is linear.
Then why does your problem statement show you maximizing alpha and
that it has bounds of [0, 1]?
| Finding a solution for this set of linear inequalities is only one step in the
| process. I'd like to write it all as a script in Octave.
|
| All tips and suggestions are welcome. Thanks
The problem you show in the image is not just a "set of linear
inequalities". It is a nonlinear optimization problem. With some
rearrangement to get your problem statement into the form accepted by
Octave's sqp function, I obtain
x =
0.538461538452721
0.307692307698186
0.153846153849093
0.749999999995322
obj = -0.749999999995322
I included alpha as a fourth decision variable, and since you are
maximizing alpha but sqp minimizes it's objective function, I used
-alpha as the objective for sqp. Here's teh code I used:
x = [1; 1; 1; 1];
function retval = phi (x)
alpha = x(4);
retval = -alpha;
endfunction
function retval = g (x)
retval = x(1) + x(2) + x(3) - 1;
endfunction
function retval = h (x)
alpha = x(4);
retval = [x(1)-(1+alpha)*x(2);
(3-alpha)*x(2)-x(1);
x(1)-(2+alpha)*x(3);
(5-2*alpha)*x(3)-x(1);
x(2)-2*x(3);
(3-alpha)*x(3)-x(2)];
endfunction
lb = [0; 0; 0; 0];
ub = [1; realmax; realmax; realmax];
[x, obj] = sqp (x, @phi, @g, @h, lb, ub)
jwe
--
A: Yes.
> Q: Are you sure?
>> A: Because it reverses the logical flow of conversation.
>>> Q: Why is top posting annoying in email?
- solving set of inequalities, mat95pat, 2010/01/23
- Re: solving set of inequalities, Jaroslav Hajek, 2010/01/23
- Re: solving set of inequalities, John W. Eaton, 2010/01/23
- Re: solving set of inequalities, Petr Korviny, 2010/01/23
- Re: solving set of inequalities, Jaroslav Hajek, 2010/01/25
- Re: solving set of inequalities, Petr Korviny, 2010/01/25
- Re: solving set of inequalities,
John W. Eaton <=
- Re: solving set of inequalities, Petr Korviny, 2010/01/25
- Re: solving set of inequalities, Jaroslav Hajek, 2010/01/26
- Re: solving set of inequalities, Jaroslav Hajek, 2010/01/26