Re: Constrained Nonlinear Optimization problem

[Ben Abbott]

On May 2, 2014, at 9:18 PM, Ether Jones <address@hidden> wrote:

> 
>  On May 2, 2014, at 7:40 PM, Ether Jones wrote:
> 
> Could someone please show me how to set up this problem in Octave?
>  
> Maximize (x + y)
>  
> Subject to constraints:
>  
>   0 <= x <= 75
>  
>   0 <= y <= 75
>  
>   29.5 - sqrt(0.184*(x+y)^2 + x^2) = 0.0
>  
>   45.5 - sqrt(0.184*(x+y)^2 + y^2) = 0.0
>  
> I have solved it with Maxima, Python, AMPL, and Excel and get the following 
> answer:
>  
>   x = 17.2
>   y = 38.7
>  
> But I'm having trouble setting it up in Octave
> Thank you.
> 
> 
> I should have made a few points clearer in my original post:
> 
> I've read the documentation for sqp() in the Octave manual.  I find it 
> puzzling.
> 
> I'm aware that maximization can be accomplished by making the objective 
> function negative ( that's what I did for Python and Maxima, using Powell's 
> COBYLA ).
> 
> I'm an Octave newbie.
> 
> This is not a homework problem (I'm in my 60's).  It's a scaled-down example 
> of a more complex engineering problem I am trying to solve.
> 
> If someone would be willing to show how to transform/convert this example 
> into the parameters that the Octave sqp() function requires it would be 
> greatly appreciated.  

Ok. My apologies. The code below solves the problem.  If the syntax isn't 
clear, feel free to ask for clarification.

phi = @(x) - sum (x);
lb = [0; 0];
ub = [75; 75];
h1 = @(x) 29.5 - sqrt (0.184 * sum (x)^2 + x(1)^2);
h2 = @(x) 45.5 - sqrt (0.184 * sum (x)^2 + x(2)^2);
h  = @(x) [h1(x); h2(x)];
x0 = [1; 1];
x  = sqp (x0, phi, [], h, lb, ub, 100, 1e-8)

Ben