what changes i need to make for better answer (fmincon)
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>> x0=[10;10;10;0.5;0.5];
>> options=optimset('Algorithm','interior-point');
>> [x,fval]=fmincon(@newfrac,x0,[],[],[],[],[0;0;0;0;0],[inf;inf;inf;0.9;0.9],@confun,options)
Local minimum found that satisfies the constraints.
Optimization completed because the objective function is non-decreasing in
feasible directions, to within the default value of the function tolerance,
and constraints were satisfied to within the default value of the constraint tolerance.
<stopping criteria details>
x =
0.0000
0.7587
0.1891
0.7928
0.9000
fval =
-22.0702
i need to reduce my function value to zero.request u tell some changes in the commands i used.
[Information merged from duplicate question]
MAIN FUNCTION
function [f] = newfrac(x)
wcg=2.1; %gain cross over frequency
bb=4;
cc=60;
r = x(1) + (x(2)*(wcg^(-x(4)))*cos(90*x(4)*(pi/180)))+ (x(3)*(wcg^(x(5)))*cos(90*x(5)*(pi/180)));
s = - x(2)*wcg^(-x(4))*sin(90*x(4)*pi/180)+ x(3)*wcg^(x(5))*sin(90*x(5)*pi/180);
fun1=bb/sqrt((cc*wcg)^2 +1);
fun2=sqrt((r)^2 + (s)^2);
f = 10*log10(fun1*fun2);
end
CONSTRAINTS PROGRAM-TO BE SATISFIED BY ABOVE FUNCTION
function [c, ceq] = confun(x)
wcg=2.1;
wt=10;
ws=0.01;
aa=2;
bb=4;
cc=60;
dd=80;
ff=0;
fipm=80; %phase margin
r = x(1) + ( x(2)*(wcg^(-x(4)))*cos(90*x(4)*(pi/180)) )+(x(3)*(wcg^(x(5)))*cos(90*x(5)*(pi/180)));
% pi/180 give degree value in radians
s = - x(2)*(wcg^(-x(4)))*sin(90*x(4)*(pi/180))+ x(3)*(wcg^(x(5)))*sin(90*x(5)*(pi/180));
ru = -x(2)*x(4)*(wcg^(-x(4)-1))*cos(90*x(4)*(pi/180))+ x(3)*x(5)*(wcg^(x(5)-1))*cos(90*x(5)*(pi/180));
su = -x(2)*x(4)*(wcg^(-x(4)-1))*sin(90*x(4)*(pi/180))+ x(3)*x(5)*(wcg^(x(5)-1))*sin(90*x(5)*(pi/180));
rt = x(1) + x(2)*(wt^((-x(4))))*cos(90*x(4)*(pi/180))+ x(3)*(wt^x(5))*cos(90*x(5)*(pi/180));
st = -x(2)*(wt^(-x(4)))*sin(90*x(4)*(pi/180))+x(3)*(wt^x(5))*sin(90*x(5)*(pi/180));
rs = x(1) + x(2)*(ws^(-x(4)))*cos(90*x(4)*(pi/180))+ x(3)*(ws^x(5))*cos(90*x(5)*(pi/180));
ss = -x(2)*(ws^(-x(4)))*sin(90*x(4)*(pi/180))+ x(3)*(ws^x(5))*sin(90*x(5)*(pi/180));
%1 equation(41)
c1 = (atan(s/r)*180/pi)-(atan(dd*wcg)*180/pi)-(wcg*ff)+180-fipm;
% 180/pi give radian value in degrees
%2 equation(42)
c21 = 1/(1+(s/r)^2);
c22 = (su*r-s*ru)/(r)^2;
c23 = dd/(1+(dd*wcg)^2);
ceq = [c1;c21*c22-c23-ff];
%3 equation(43)
c31 = aa*sqrt((rt^2) + (st^2));
c32 = sqrt((1+aa*rt)^2 + (dd*wt+aa*st)^2);
c3 = (10*log10(c31/c32))+20;
%4 equation(44)
c41 = sqrt((cc*ws)^2 +1);
c42 = sqrt((1+bb*rs)^2+(cc*ws+bb*ss)^2);
c4 = (10*log10(c41/c42))+20;
c=[c3;c4];
end
SIR THESE TWO ARE PROGRAMS I HAVE WRITTEN IN MATLAB,THE COMMANDS I USED ARE
>> f_obj=@(x)newfrac(x)^2;
>> x0=[10;10;10;0.5;0.5];
>> options=optimset('Algorithm','interior-point');
>> [x,fval]=fmincon(f_obj,x0,[],[],[],[],[0;0;0;0;0],[inf;inf;inf;0.9;0.9],@confun,options)
Local minimum found that satisfies the constraints.
Optimization completed because the objective function is non-decreasing in
feasible directions, to within the default value of the function tolerance,
and constraints were satisfied to within the default value of the constraint tolerance.
<stopping criteria details>
x =
1.2403
3.0557
0.4837
0.4822
0.9000
fval =
104.6186
>> [x,fval]=fmincon(@newfrac,x0,[],[],[],[],[0;0;0;0;0],[inf;inf;inf;0.9;0.9],@confun,options)
Local minimum found that satisfies the constraints.
Optimization completed because the objective function is non-decreasing in
feasible directions, to within the default value of the function tolerance,
and constraints were satisfied to within the default value of the constraint tolerance.
<stopping criteria details>
x =
0.0000
0.7587
0.1891
0.7928
0.9000
fval =
-22.0702
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Antworten (2)
Sargondjani
am 17 Mai 2012
-22 is better than 0, so the solution fmincon found is better than what you want... why would you want 0 if the optimum (lowest possible value) is -22???
if you dont want the minimum but find the zero of the funciton, than you should use 'fsolve'
16 Kommentare
Sargondjani
am 19 Mai 2012
this doesnt mean anything to me... all i know is that matlab seems to do the optimization properly, so first you need to find out what you want the optimizer to do, and maybe change the initial guess.
and do you know if the problem is well-behaved?? if it is not, you should try loads of initial guess...
Elizabeth
am 30 Jul. 2012
Bearbeitet: Elizabeth
am 30 Jul. 2012
Hello sir, I obtained what I assume to be the correct result for your program:
Local minimum found that satisfies the constraints.
Optimization completed because the objective function is non-decreasing in
feasible directions, to within the default value of the function tolerance,
and constraints are satisfied to within the default value of the constraint tolerance.
<stopping criteria details>
x =
0.3348
2.5203
0.5623
0.5791
0.8251
fval =
1.5559e-013
I obtained this result my manipulating the logarithm function in you objective function. You can now write it as follows:
function [f] = newfrac(x)
wcg=2.1; %gain cross over frequency
bb=4;
cc=60;
r = x(1) + (x(2)*(wcg^(-x(4)))*cos(90*x(4)*(pi/180)))+ (x(3)*(wcg^(x(5)))*cos(90*x(5)*(pi/180)));
s = - x(2)*wcg^(-x(4))*sin(90*x(4)*pi/180)+ x(3)*wcg^(x(5))*sin(90*x(5)*pi/180);
fun1=bb/sqrt((cc*wcg)^2 +1);
fun2=sqrt((r)^2 + (s)^2);
fun_x=fun1*fun2;
origf=10*log10(fun_x);
f= 10^origf;
end
PROOF: ****************************************************************
===> For purposes of our discussion, Let:
x = fun_x = fun1*fun2
b = 10 (our base of the log)
k = 10 (the constant)
y= origf (the original expression for the objective function)
===> Therefore, the original function f that you had can be written as
y=k*logb(x) (EQ1)
===> By the properties of logarithmic functions, then
y= b^[klogb(x)]=x (EQ2)
===> Meanwhile, the following theorem must hold true
y=k*logb(x) if and only if b^y=x EQ(3)
===> Using EQs (1-3) and substitution, one can see--
y=k*logb(x)=b^[klogb(x)]
===> Or, in other words,
y=origf=10*log10(fun_x) EQ(4)
iff y=10^[10*log10(fun_x)=f (EQ5)
===> and so, we note EQ(4) is equivalent to EQ(5), but EQ(4) is ill-conditioned in comparison to EQ(5). ***************************************************** In conclusion, the only issue I think you need to correct is to rewrite your objective function in the form of EQ(5)
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