Re: minimization problem, sqp

[Juan Pablo Carbajal]

On Thu, Feb 28, 2013 at 2:24 PM, Urs Hackstein
<address@hidden> wrote:
> Hi Juan,
>
> thanks a lot for your explanations. If I understand you correctly, my script
> should be the following:
>
> function erg=funp(x,p)
> erg=(p(1)-x(1).*p(2)-x(2).*p(3)-x(3).*p(4)-x(4).*p(5)-x(5).*p(6)-x(6).*p(7)-x(7).*p(8)).^2
> endfunction
>
> function minimi=minimize(b,ps1,ps2,ps3,ps4,ps5,ps6,ps7)
> global b;
> global ps1;
> global ps2;
> global ps3;
> global ps4;
> global ps5;
> global ps6;
> global ps7;
> a1=b; a2=ps1; a3=ps2; a4=ps3; a5=ps4; a6=ps5; a7=ps6; a8=ps7;
> funpwrap=@(x)funp(x,[a1,a2,a3,a4,a5,a6,a7,a8])
> minimi=sqp([0;0;0;0;0;0;0],funpwrap,[-1;-1;-1;-1;-1;-1;-1],[1;1;1;1;1;1;1])
> endfunction
>
> But if  I call minimize(2,1,0,0,0,0,0,0), I receive the following error:
> funpwrap =
>
> @(x) funp (x, [a1, a2, a3, a4, a5, a6, a7, a8])
>
> error: A(I): Index exceeds matrix dimension.
> error: called from:
> error:   /home/hackstein/Dominantepole/funp.m at line 2, column 4
> error:    at line -1, column -1
> error:   /usr/share/octave/3.2.4/m/optimization/sqp.m at line 347, column 9
> error:   /home/hackstein/Dominantepole/minimize.m at line 12, column 7
>
> How can we get rid of this error?
>
>
> 2013/2/28 Juan Pablo Carbajal <address@hidden>
>>
>> On Mon, Feb 25, 2013 at 4:37 PM, Urs Hackstein
>> <address@hidden> wrote:
>> > Juan,
>> >
>> > I read the manual before posting my question (my attempt was the result
>> > of
>> > reading it) and I did it again, but it didn't help. I still get the
>> > error
>> > "`b' undefined near line 3 column 6" and don't know how to fix it.
>> > Perhaps
>> > the problem is that fun is not just a function of x, but also of b and
>> > the
>> > psj, but, as I said, I don't know how to fix it.
>> >
>> >
>> > 2013/2/25 Juan Pablo Carbajal <address@hidden>
>> >>
>> >> On Mon, Feb 25, 2013 at 3:32 PM, Urs Hackstein
>> >> <address@hidden> wrote:
>> >> >
>> >> >
>> >> > ---------- Forwarded message ----------
>> >> > From: Urs Hackstein <address@hidden>
>> >> > Date: 2013/2/25
>> >> > Subject: Re: minimization problem, sqp
>> >> > To: Juan Pablo Carbajal <address@hidden>
>> >> >
>> >> >
>> >> > Hi Juan,
>> >> >
>> >> > the problem is that my attempt does not work and I am not familiar
>> >> > enough
>> >> > with the sqp syntax to get the x(1),...,x(7) as output. Thus any
>> >> > suggestions
>> >> > for a correct program?
>> >> >
>> >> >
>> >> > Sincerely yours,
>> >> >
>> >> > Urs Hackstein
>> >> >
>> >> > 2013/2/25 Juan Pablo Carbajal <address@hidden>
>> >> >>
>> >> >> On Mon, Feb 25, 2013 at 2:30 PM, Urs Hackstein
>> >> >> <address@hidden> wrote:
>> >> >> > Dear list,
>> >> >> >
>> >> >> > I am relatively new to octave and dealing with the following
>> >> >> > minimization
>> >> >> > problem:
>> >> >> > Let b, ps1, ps2, ps3, ps4, ps5, ps6 and ps7 arbitrary complex
>> >> >> > numbers.
>> >> >> > My
>> >> >> > goal is to determine the real numbers x(1), x(2), x(3),
>> >> >> > x(4),x(5),x(6),x(7)
>> >> >> > with -1<=x(j)<=1, j=1,..,7, such that the function
>> >> >> >
>> >> >> >
>> >> >> >
>> >> >> >
>> >> >> > (b-x(1).*ps1-x(2).*ps2-x(3).*ps3-x(4).*ps4-x(5).*ps5-x(6).*ps6-x(7).*ps7).^2
>> >> >> > takes its minimal value.
>> >> >> >
>> >> >> > I made the following attempt using sqp:
>> >> >> >
>> >> >> > function erg=fun(x)
>> >> >> >
>> >> >> >
>> >> >> >
>> >> >> > erg=(b-x(1).*ps1-x(2).*ps2-x(3).*ps3-x(4).*ps4-x(5).*ps5-x(6).*ps6-x(7).*ps7).^2
>> >> >> > endfunction
>> >> >> >
>> >> >> > function minimi=minimize(b,ps1,ps2,ps3,ps4,ps5,ps6,ps7)
>> >> >> > global b;
>> >> >> >
>> >> >> >
>> >> >> > minimi=sqp([0;0;0;0;0;0;0],@fun,[-1;-1;-1;-1;-1;-1;-1],[1;1;1;1;1;1;1])
>> >> >> > endfunction
>> >> >> >
>> >> >> > Thanks a lot in advance!
>> >> >> >
>> >> >> > Sincerely yours,
>> >> >> >
>> >> >> > Urs Hackstein
>> >> >> >
>> >> >> > _______________________________________________
>> >> >> > Help-octave mailing list
>> >> >> > address@hidden
>> >> >> > https://mailman.cae.wisc.edu/listinfo/help-octave
>> >> >> >
>> >> >>
>> >> >>  Hi Urs,
>> >> >>
>> >> >> Great! and what is the problem?
>> >> >
>> >> >
>> >> >
>> >> >
>> >> > _______________________________________________
>> >> > Help-octave mailing list
>> >> > address@hidden
>> >> > https://mailman.cae.wisc.edu/listinfo/help-octave
>> >> >
>> >>
>> >> Urs,
>> >>
>> >> Ok, have you try reading the help of sqp?
>> >> > help sqp
>> >>
>> >> If you have questions after reading that we can help you, but do
>> >> please read the manual. also search the web, there are plenty of
>> >> examples using sqp
>> >
>> >
>>
>> Hi Urs,
>>
>> Yes, that may be a problem. Lets say you want of din the minimum of the
>> function
>>
>> f(x; a, b) = x*(a*x + b)
>>
>> The function is parametrized by a and b, i.e. it represents a family
>> of functions. To optimize you have to specify which one you want to
>> work with.
>> So we create the parametrized function
>>
>> function y = f (x, p)
>>   y = x .* (p(1)*x + p(2));
>> endfunction
>>
>> Before we can pass it to sqp we have to define the values of the
>> parameters, one way of doing that is using a wrapper (I think is the
>> recommended way, though it may be less efficient than other ways, but
>> do not know for how much)
>>
>> a = 1; b = -1;
>> fwrap = @(x) f (x,[a,b])
>>
>> Then we can call sqp
>>
>>  sqp (2*rand(1)-1, fwrap)
>>
>> and I get
>>
>> ans =  0.50000
>>
>> as expected.
>>
>> Hope this solves your problem
>
>

First, If you use the me wrapper method you do not need the global
variables nor the minimize function.

function erg = funp(x,p)
  erg = ( p(1) - p(2:end) * x(:) ).^2
endfunction

funpwrap = @(x)funp(x,[b,ps1,ps2,ps3,ps4,ps5,ps6,ps7])
x0  = zeros (7,1);
lbound = -1;
ubound = 1;
sqp (x0, funpwrap,[],[],lbound,ubound)

Now, read the help of sqp again more carefully, I think you haven't
payed enough attention.